Linearity

Problem 4501

15. What is the solution to $4(y-3)+19=8(2 y+3)+7$ ?

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Problem 4502

8. Examine the rectangle shown and write down two equations in $x$ and $y$ . Now solve these equations to find the value of $x$ and the value of $y$ .

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Problem 4503

11. Three chocolate bars and four chocolate eggs weigh 465 grams. Three chocolate bars and two chocolate eggs weigh 315 grams. (i) Which of these pairs of equations is correct for the chocolate bars and eggs? (A) $\begin{array}{l} 3 b+2 e=465 \\ 3 b+4 e=315 \end{array}$
B $\begin{array}{l} b+4 e=465 \\ b+2 e=315 \end{array}$ $3 b+4 e=465$ $3 b+2 e=315$ (ii) Solve the pair of simultaneous equations that is correct to find the values of $b$ and $e$ .

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Problem 4504

ion 3.3 Question 8, 3.3.B-6 Part 3 of 8
Find the solution(s) in the set $W$ for each of the following parts a) th A. 7 B. 5 C. 6 D. 8 b) $(11-x)-5=1$ A. 6 - 8 C. 5
0. 7 c) $7+x=x+7$ A. 7

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Problem 4505

Find the $x$ - and $y$ -intercepts of the graph of $3 x-4 y=27$ . State each answer as an integer or an improper fraction in simplest form.
Answer Attempt 1 out of 2 x-intercept: $\square$ y-intercept: $\square$

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Problem 4506

Find the slope and the $y$ -intercept of the line. 17) $y=-7 x-6$

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Problem 4507

Solve the system of equations. $\begin{array}{c} 4 x-5 y+2 z=-8 \\ 12 x-15 y+6 z=1 \\ 2 x-4 y-5 z=4 \end{array}$
Select the correct choice below and fill in any answer boxes within your choice. A. There is one solution. The solution is (, $\square$ , , (Type exact answers in simplified form.) B. There are infinitely many solutions. The solutions are $(, z, y$ , where $z$ is any real number. (Type exact answers in simplified form.) C. There is no solution.

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Problem 4508

Solve the following system of equations. $\begin{array}{l} \frac{1}{6} x-\frac{1}{3} y=-4 \\ \frac{1}{4} x+\frac{3}{5} y=5 \end{array}$ $\begin{array}{l} x=\square \\ y=\square \end{array}$

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Problem 4509

The admission fee at a local zoo is $\$ 1.50$ for children and $\$ 7.00$ for adults. On a certain day, 2200 people enter the zoo and $\$ 11,550.00$ is collected. How many children and how many adults attended?
How many children attended?: $\square$ How many adults attended: $\square$ Question Help: Video Message instructor Submit Question

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Problem 4510

Solving a percent mixture problem using a system of linear equations
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is $35 \%$ salt and Solution B is $85 \%$ salt. She wants to obtain 40 ounces of a mixture that is $45 \%$ salt. How many ounces of each solution should she use?
Note that the ALEKS graphing calculator can be used to make computations easier.
Solution A: $\square$ ounces
Solution B: $\square$ ounces

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Problem 4511

Which equation represents the same line as the points in the table? \begin{tabular}{|c|c|} \hline Input (x) & Output $(y)$ \\ \hline-4 & 5 \\ \hline 0 & 2 \\ \hline $\frac{8}{3}$ & 0 \\ \hline \end{tabular} $y=-\frac{3}{4} x+\frac{8}{3}$ $y=-\frac{3}{4} x+2$ $y=2 x-\frac{3}{4}$ $y=-3 x+2$

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Problem 4512

Use the distributive property to find an equivalent expression: $6(4+2 t)=$ $\square$
DO NOT USE ANY SPACES BETWEEN THE NUMBERS OR OPERATION S

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Problem 4513

Find an equivalent expression (use the "reverse" method) DO NOT TYPE SPACES $8 u+32=$

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Problem 4514

Find an equivalent expression (use the "reverse" method) DO NOT TYPE SPACES $8 u+32=$

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Problem 4515

3 Exercice 3 : Equations simples Résoudre les équations suivantes, si la solution est sous la forme d'un fraction, donner la forme irréductible a. $12 \mathrm{x}-8=4$ b. $\frac{x}{6}+12=2 \mathrm{x}-4$
3. $4 \mathrm{x}+5=-11 \mathrm{x}-5$

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Problem 4516

$\begin{array}{c}\left\{\begin{array}{l}2 x+5 y-27=0 \\ -2 x+27=5 y\end{array}\right. \\ (x, y)=(\square)\end{array}$

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Problem 4517

Solve the inequallity. Graph your solution.
9. $\frac{x}{-10} \leq 22$
13. $1.6 x \leq-11.2$
17. $\frac{x}{1.3} \geq 7.1$
21. $-0.1 x \leq-2.5$
22. $-9.8 x \geq 44.1$
11. $-13 x<-208$
15. $-10.7>\frac{x}{-4}$
19. $-3.8 x \geq 28.5$
23. $\frac{x}{-12.7} \geq-2.2$
12. $45 x \leq-855$
16. $8.3 \leq \frac{x}{-5}$
20. $10.4 x>520$
24. $\frac{x}{4.2}<-20.45$

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Problem 4518

Set up the problem shown below and use Solver to verify that you will get $\$ 5,266.67$ in interest per year.
You have $\$ 120,000$ to invest in 4 CDs. The rates are shown in the following table: \begin{tabular}{|l|l|l|} \hline CDs & Amount Invested & Interest Rate \\ \hline A & $\$$ - & $3 \%$ \\ \hline B & $\$-$ & $4 \%$ \\ \hline C & $\$-$ & $4.50 \%$ \\ \hline D & $\$-$ & $5 \%$ \\ \hline \end{tabular}
There is a constraint that the money invested in CD B be exactly twice the amount of money invested in CD A. This means that you can dispense with one of the decision variables.

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Problem 4519

15. For a summer landscaping job Jalen makes $\$ 17$ per hour plus a bonus of $\$ 1.50$ for each lawn that he cuts. How much would Jalen make if he cuts 36 lawns while working 42 hours in one week? Create an equation and then solve the problem.

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Problem 4520

A video is made of a train traveling 20 feet per second. If the video is played in reverse, describe the location of the train after 4 seconds.

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Problem 4521

Work the problem and type the correct answer into the box below. (round answer to one decimal place) $\begin{array}{l} 15.3+x=17.7 \\ x=\square \end{array}$

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Problem 4522

Solve the equation: $-11 x+6-5(x-1)=-5 x-(10 x-4)+5$ . Is it an identity, contradiction, or find the solution set?

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Problem 4523

Solve the equation using addition and multiplication principles:
$5[7-5(6-r)]-7=7[5(7 r-6)+4]-50$
What is the solution? A. $r=\square$ , B. all real numbers, C. no solution.

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Problem 4524

Solve the inequalities $8-3x>5$ and $x-5 \geq 10$ , then sketch the solution.

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Problem 4525

Solve the compound inequality and graph the solution: $3x - 9 > 0$ and $-4x + 9 < 5$ . Provide the solution in interval notation.

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Problem 4526

Solve the equation: $\frac{3 x+23}{7}+\frac{x+36}{5}=13$ . Provide an integer or simplified fraction as the solution.

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Problem 4527

Solve: $-7<\frac{4 x-5}{6}<2$ . Choose A, B, C, D, E, or F for the solution set.

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Problem 4528

Solve the inequality $-3<\frac{4 x-5}{6}<1$ and choose the correct solution set.

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Problem 4529

Solve the compound inequality: $-17 < 2y - 3 \leq 3$ .

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Problem 4530

Solve the compound inequality $-17 < 2y - 3 \leq 3$ and express the solution in interval notation. Use decimal values.

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Problem 4531

Solve the compound inequality $-41 < 4n - 1 \leq 31$ and graph the solution set.

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Problem 4532

Graph the solution for the inequality $x \geq 5$ .

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Problem 4533

Comet A's orbit is 187 years, 17 times Comet B's. Find Comet B's orbit length.

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Problem 4534

Solve the inequality $6z - 26.4 < -22 + 5z$ and express the solution in interval notation using decimals.

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Problem 4535

Solve the inequality $6z - 26.4 < -22 + 5z$ and graph the solution set.

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Problem 4536

Solve the inequality $6x - 13.2 < -11 + 5x$ and graph the solution set.

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Problem 4537

Find three consecutive odd integers where the sum of the first, twice the second, and three times the third equals 22. The smallest is 1. What is the second largest?

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Problem 4538

Find three consecutive odd integers where the sum of the first, twice the second, and three times the third equals 22.

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Problem 4539

Solve for g in the equation C = (g + w) / 2.

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Problem 4540

Find $\mathbf{u}+\mathbf{v}$ and $\mathbf{u}-3 \mathbf{v}$ for $u=\begin{bmatrix}-3 \\ 6\end{bmatrix}, v=\begin{bmatrix}-5 \\ 4\end{bmatrix}$ .

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Problem 4541

Find $\mathbf{u}+\mathbf{v}$ and $\mathbf{u}-3 \mathbf{v}$ for $u=\begin{bmatrix}-3 \\ 6\end{bmatrix}$ and $v=\begin{bmatrix}-5 \\ 4\end{bmatrix}$ .

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Problem 4542

Write a system of equations for the vector equation $x_{1}\begin{bmatrix} 3 \\ -3 \\ 7 \end{bmatrix} + x_{2}\begin{bmatrix} 6 \\ 0 \\ -6 \end{bmatrix} = \begin{bmatrix} 4 \\ -2 \\ 8 \end{bmatrix}$ . Choose the correct option.

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Problem 4543

Is vector $b$ a linear combination of $a_{1}, a_{2}, a_{3}$ ? Choose A, B, C, or D based on the echelon matrix pivots.

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Problem 4544

Is the vector $u=\begin{bmatrix}-7 \\ 10 \\ 8\end{bmatrix}$ in the plane spanned by the columns of $A=\begin{bmatrix}2 & -4 \\ -5 & 7 \\ 2 & 2\end{bmatrix}$ ? Explain.

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Problem 4545

Solve the inequality: $-7(x-5)>3x-5$ . Provide the solution set in interval notation and graph form.

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Problem 4546

Draw a line to model Chicago's population growth from 1880 (500,000) to 1930 (3,400,000) and find its equation.

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Problem 4547

Solve the compound inequality: $x-3 \leq 6$ and $x+1 \geq 5$ . Provide the solution in interval and graph forms.

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Problem 4548

Solve the equation: $2(9r + 17) = 16r + 6$ . Fill in the blanks and simplify each step.

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Problem 4549

Find a number $x$ such that $\frac{1}{4}x + 10 \geq 3$ . What is the solution set in interval notation?

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Problem 4550

Solve the equation: $3x - 5 = 7x + 11$ . What is the solution set? Choose A, B, or C.

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Problem 4551

Solve the equation: $0.95 x - 0.99 = 12.93 - 3.85 x$ . What is $x$ ? A. $x=\square$ , B. all real numbers, C. no solution.

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Problem 4552

Do the vectors $\mathbf{v}_{1} = \begin{bmatrix} 0 \\ 0 \\ -3 \end{bmatrix}$ , $\mathbf{v}_{2} = \begin{bmatrix} 0 \\ -5 \\ 6 \end{bmatrix}$ , and $\mathbf{v}_{3} = \begin{bmatrix} 5 \\ -3 \\ 9 \end{bmatrix}$ span $\mathbb{R}^{3$? Explain.

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Problem 4553

Graph the functions $f$ and $g$ for $x$ from -2 to 2, then describe how $g$ relates to $f$ . Examples:
39. $f(x)=x, g(x)=x+3$
40. $f(x)=x, g(x)=x-4$
41. $f(x)=-2x, g(x)=-2x-1$
42. $f(x)=-2x, g(x)=-2x+3$
43. $f(x)=x^{2}, g(x)=x^{2}+1$
44. $f(x)=x^{2}, g(x)=x^{2}-2$
45. $f(x)=|x|, g(x)=|x|-2$

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Problem 4554

Create an equation for this: 19 minus $\frac{5}{3}$ of a number equals 4. Solve for $x$ . Options: A. $19-\frac{5}{3} x=4$ B. $\frac{5}{3}-19 x=4$ C. $19-\frac{5}{3}=4$ D. $5 \frac{5}{3} x-19=4$ . Find $x$ .

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Problem 4555

Solve the inequality $4z - 9.6 < -7.2 + 3z$ and express the solution in interval notation using decimals.

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Problem 4556

Solve for $p$ in the equation: $-15 p - 4(6 - 6 p) = 6(p - 3) - 3$ . What is the solution set? A, B, or C?

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Problem 4557

Solve the inequality $-4 \leq -2x + 2 < 10$ and express the solution in interval notation.

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Problem 4558

Solve the compound inequality: $-2x < -6$ and $x - 2 < 8$ . What is the solution? A. $x<$ B. $x>$ C. All real numbers. D. No solution.

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Problem 4559

Find angles A and B where $A + B = 90^{\circ}$ and $A = 2B + 24^{\circ}$ . What are the measures of A and B?

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Problem 4560

Solve the equation: $2(9r + 17) = 16r + 6$ . Fill in the missing terms and simplify fractions.

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Problem 4561

A meal has 75g Carbs, 20g Protein, and 605 total calories. Find grams of Fat. Options: a) 15 b) 25 c) 35 d) 40.

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Problem 4562

Solve the equation: $\frac{2}{7}(5 x+4)=\frac{1}{2}(3 x-26)+12$ . What is $x$ ? A. $x=\square$ B. All real numbers. C. No solution.

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Problem 4563

Solve the compound inequality $x<2$ or $x<5$ and graph $x<2$ . Choose the correct graph from options A, B, C, or D.

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Problem 4564

Solve the compound inequality $x+1>6$ or $4-x>5$ . Provide the solution set in interval and graph forms.

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Problem 4565

Solve the equation step-by-step, filling in missing terms and simplifying fractions:
$7(4b + 2) + 17b = 14$
Find $b$ after applying the distributive property and combining like terms.

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Problem 4566

Solve the equation step by step. Fill in the blanks and simplify.
$\begin{aligned} -2(-19 w-14) & =-10 \\ \square+28 & =-10 \\ 38 w & = \\ w & = \end{aligned}$

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Problem 4567

Solve for $y$ in the equation: $3y + 15 - 7 = 14$ .

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Problem 4568

Solve the equation step by step and fill in the missing terms. Simplify fractions where needed.
$6(13 w+2)-10=2$
$\square+12-10=2$
$78 w+\square=2$
Find $w$ by applying the distributive property and combining like terms.

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Problem 4569

Solve the equation and fill in the missing terms:
$3y + 15 - 7 = 14$
Complete:
$3y + \square = 14$
$3y = \square$
$y = \square$

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Problem 4570

Solve the equation: $-5(-2x-17)=-5$ . Find $x$ and simplify.

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Problem 4571

Solve the equation: $-2c + 2 + 11 = 11$ . Find $c$ after simplifying.

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Problem 4572

Solve the equation: $7(8 s+1) =s+7$ . Fill in missing terms and simplify to find $s =$ .

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Problem 4573

Solve the compound inequality: $3(x-4)<15$ or $x+10>14$ . What are the solution options?

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Problem 4574

Solve the equation: -6b + 6 = -2b + 6. Find missing values and simplify. $-4b = \square, \; b = \square$ .

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Problem 4575

Solve the equation and fill in the blanks. Simplify fractions:
$\begin{aligned} 16 q-8-20 q & =16 \\ \square-8 & =16 \\ -4 q & =\square \\ q & =\square \end{aligned}$

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Problem 4576

Solve the equation and fill in missing terms. Simplify fractions.
$-8 y-16-5 y =-5 y+8 \\ -13 y-16 =-5 y+8 \\ -8 y-16 =8 \\ -8 y =\square \\ y =$
Divide both sides by -8.

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Problem 4577

How many miles must you travel for Taxi 2 ( $\$ 4.50 + \$ 1.75 \cdot x$ ) to cost less than Taxi 1 ( $\$ 2.75 + \$ 2.00 \cdot x$ )?

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Problem 4578

Solve the equation step by step. Fill in missing terms and simplify:
$4(15 r+5)-6 = 14$
Find $r$ .

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Problem 4579

Solve the equation: $6(10r+1)=6$ . Find $r$ and simplify any fractions.

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Problem 4580

Solve the equation step by step and simplify any fractions. Find $a$ in $53 a = 0$ . What is $a$ ?

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Problem 4581

Find all three-digit numbers where the first digit is 4 less than the second and the third digit is 2 more than the first.

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Problem 4582

Solve the equation step by step and fill in missing terms: $4(7d+2)+6=14$ . Simplify fractions where needed.

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Problem 4583

Find the difference quotient for the function $f(x)=-4x+7$ : $\frac{f(x+h)-f(x)}{h}, h \neq 0$ . Simplify your answer.

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Problem 4584

Solve the equation for $r$ :
$19r + 2 + 17r = 13r + 2$
Simplify and fill in the missing steps.

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Problem 4585

Solve the equation and fill in the missing terms:
5v + 15 = 3v + 17
Subtract 3v:
2v = \square
Subtract 15:
v = \square (Divide by 2)

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Problem 4586

Solve the equation step-by-step and fill in the blanks:
$19 r+2+17 r= 13 r+2$ $36 r+2 =13 r+2$ $23 r+2 =2$ $23 r =\square$ $r =\square$

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Problem 4587

Solve the equation: $19r + 2 + 17r = 13r + 2$ . Simplify fractions and find $r$ .

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Problem 4588

Solve the equation: $2(14d + 4) = 15d + 8$ . Simplify and find $d$ .

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Problem 4589

Solve the equations: 3q + 6 = q + 8 and 2q + 6 = 8. Find $2q=$ , $q=$ , and simplify fractions.

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Problem 4590

Solve the equation: $16w + 17 + 14w = 17$ . Simplify and find $w$ . What is $w = \square$ ?

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Problem 4591

Solve the equation and find $p$ in the steps below. Simplify any fractions.
$17 p+1+p =19 \\ 18 p+1 =19 \\ 18 p =18 \\ p =\square \quad \text{(Divide both sides by 18)}$

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Problem 4592

Solve the equation step by step and find $b$ . Fill in missing terms and simplify.
$2(3 b+5)+12 b =13 b+15$

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Problem 4593

Solve the equation: $3(x+3)+x = 2x+15$ . Fill in missing terms and simplify fractions. Find $x$ .

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Problem 4594

Bert made 3 batches of sauce using 24 ounces total, reducing hot sauce by 2 ounces per batch. Find $u$ : usual amount per batch.
Which equation to use? $3(u-2)=24$ $3 u-2=24$ $2 u-3=24$ $2(u-3)=24$
What is $u$ ? Answer in ounces.

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Problem 4595

Solve the system of equations: $x - 5y = 8$ and $-7x + 8y = 25$ .

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Problem 4596

Ms. Garza ordered 9 cases of caramel apples, sold 685, and had 35 left. What equation finds apples per case? $9c - 685 = 35$

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Problem 4597

Rhianna buys 6 chairs for \ $455 after a \$55 discount. Find the equation for the regular cost,$ c$, of each chair.

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Problem 4598

The Logan family rents a beach house for 9 days, paying \ $920 after a \$25 discount. Find the daily charge$ d$:
$9d - 25 = 920$

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Problem 4599

Simplify the expression: $7(y-9)-2y$ .

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Problem 4600

Solve the system of equations: $3a - 2b = 13$ and $2a + 4b = 13$ .

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1 ...43 44 45 46 47 48 49 ...77

Linearity

Problem 4501

15. What is the solution to 4(y−3)+19=8(2y+3)+74(y-3)+19=8(2 y+3)+74(y−3)+19=8(2y+3)+7 ?

Problem 4502

8. Examine the rectangle shown and write down two equations in xxx and yyy. Now solve these equations to find the value of xxx and the value of yyy.

Problem 4503

Problem 4504

ion 3.3 Question 8, 3.3.B-6 Part 3 of 8Find the solution(s) in the set WWW for each of the following parts a) th A. 7 B. 5 C. 6 D. 8 b) (11−x)−5=1(11-x)-5=1(11−x)−5=1 A. 6 - 8 C. 50. 7 c) 7+x=x+77+x=x+77+x=x+7 A. 7

Problem 4505

Find the xxx - and yyy-intercepts of the graph of 3x−4y=273 x-4 y=273x−4y=27. State each answer as an integer or an improper fraction in simplest form.Answer Attempt 1 out of 2 x-intercept: □\square□ y-intercept: □\square□

Problem 4506

Find the slope and the yyy-intercept of the line. 17) y=−7x−6y=-7 x-6y=−7x−6

Problem 4507

Problem 4508

Solve the following system of equations. 16x−13y=−414x+35y=5\begin{array}{l} \frac{1}{6} x-\frac{1}{3} y=-4 \\ \frac{1}{4} x+\frac{3}{5} y=5 \end{array}61​x−31​y=−441​x+53​y=5​ x=□y=□\begin{array}{l} x=\square \\ y=\square \end{array}x=□y=□​

Problem 4509

Problem 4510

Problem 4511

Problem 4512

Use the distributive property to find an equivalent expression: 6(4+2t)=6(4+2 t)=6(4+2t)= □\square□DO NOT USE ANY SPACES BETWEEN THE NUMBERS OR OPERATION S

Problem 4513

Find an equivalent expression (use the "reverse" method) DO NOT TYPE SPACES 8u+32=8 u+32=8u+32=

Problem 4514

Find an equivalent expression (use the "reverse" method) DO NOT TYPE SPACES 8u+32=8 u+32=8u+32=

Problem 4515

Problem 4516

{2x+5y−27=0−2x+27=5y(x,y)=(□)\begin{array}{c}\left\{\begin{array}{l}2 x+5 y-27=0 \\ -2 x+27=5 y\end{array}\right. \\ (x, y)=(\square)\end{array}{2x+5y−27=0−2x+27=5y​(x,y)=(□)​

Problem 4517

Problem 4518

Problem 4519

15. For a summer landscaping job Jalen makes $17\$ 17$17 per hour plus a bonus of $1.50\$ 1.50$1.50 for each lawn that he cuts. How much would Jalen make if he cuts 36 lawns while working 42 hours in one week? Create an equation and then solve the problem.

Problem 4520

A video is made of a train traveling 20 feet per second. If the video is played in reverse, describe the location of the train after 4 seconds.

Problem 4521

Work the problem and type the correct answer into the box below. (round answer to one decimal place) 15.3+x=17.7x=□\begin{array}{l} 15.3+x=17.7 \\ x=\square \end{array}15.3+x=17.7x=□​

Problem 4522

Solve the equation: −11x+6−5(x−1)=−5x−(10x−4)+5-11 x+6-5(x-1)=-5 x-(10 x-4)+5−11x+6−5(x−1)=−5x−(10x−4)+5. Is it an identity, contradiction, or find the solution set?

Problem 4523

Solve the equation using addition and multiplication principles: 5[7−5(6−r)]−7=7[5(7r−6)+4]−50 5[7-5(6-r)]-7=7[5(7 r-6)+4]-50 5[7−5(6−r)]−7=7[5(7r−6)+4]−50 What is the solution? A. r=□r=\squarer=□, B. all real numbers, C. no solution.

Problem 4524

Solve the inequalities 8−3x>58-3x>58−3x>5 and x−5≥10x-5 \geq 10x−5≥10, then sketch the solution.

Problem 4525

Solve the compound inequality and graph the solution: 3x−9>03x - 9 > 03x−9>0 and −4x+9<5-4x + 9 < 5−4x+9<5. Provide the solution in interval notation.

Problem 4526

Solve the equation: 3x+237+x+365=13\frac{3 x+23}{7}+\frac{x+36}{5}=1373x+23​+5x+36​=13. Provide an integer or simplified fraction as the solution.

Problem 4527

Solve: −7<4x−56<2-7<\frac{4 x-5}{6}<2−7<64x−5​<2. Choose A, B, C, D, E, or F for the solution set.

Problem 4528

Solve the inequality −3<4x−56<1-3<\frac{4 x-5}{6}<1−3<64x−5​<1 and choose the correct solution set.

Problem 4529

Solve the compound inequality: −17<2y−3≤3-17 < 2y - 3 \leq 3−17<2y−3≤3.

Problem 4530

Solve the compound inequality −17<2y−3≤3-17 < 2y - 3 \leq 3−17<2y−3≤3 and express the solution in interval notation. Use decimal values.

Problem 4531

Solve the compound inequality −41<4n−1≤31-41 < 4n - 1 \leq 31−41<4n−1≤31 and graph the solution set.

Problem 4532

Graph the solution for the inequality x≥5x \geq 5x≥5.

Problem 4533

Comet A's orbit is 187 years, 17 times Comet B's. Find Comet B's orbit length.

Problem 4534

Solve the inequality 6z−26.4<−22+5z6z - 26.4 < -22 + 5z6z−26.4<−22+5z and express the solution in interval notation using decimals.

Problem 4535

Solve the inequality 6z−26.4<−22+5z6z - 26.4 < -22 + 5z6z−26.4<−22+5z and graph the solution set.

Problem 4536

Solve the inequality 6x−13.2<−11+5x6x - 13.2 < -11 + 5x6x−13.2<−11+5x and graph the solution set.

Problem 4537

Find three consecutive odd integers where the sum of the first, twice the second, and three times the third equals 22. The smallest is 1. What is the second largest?

Problem 4538

Find three consecutive odd integers where the sum of the first, twice the second, and three times the third equals 22.

Problem 4539

Solve for g in the equation C = (g + w) / 2.

Problem 4540

Find u+v\mathbf{u}+\mathbf{v}u+v and u−3v\mathbf{u}-3 \mathbf{v}u−3v for u=[−36],v=[−54]u=\begin{bmatrix}-3 \\ 6\end{bmatrix}, v=\begin{bmatrix}-5 \\ 4\end{bmatrix}u=[−36​],v=[−54​].

Problem 4541

Find u+v\mathbf{u}+\mathbf{v}u+v and u−3v\mathbf{u}-3 \mathbf{v}u−3v for u=[−36]u=\begin{bmatrix}-3 \\ 6\end{bmatrix}u=[−36​] and v=[−54]v=\begin{bmatrix}-5 \\ 4\end{bmatrix}v=[−54​].

Problem 4542

Problem 4543

Is vector bbb a linear combination of a1,a2,a3a_{1}, a_{2}, a_{3}a1​,a2​,a3​? Choose A, B, C, or D based on the echelon matrix pivots.

Problem 4544

Is the vector u=[−7108]u=\begin{bmatrix}-7 \\ 10 \\ 8\end{bmatrix}u=⎣⎡​−7108​⎦⎤​ in the plane spanned by the columns of A=[2−4−5722]A=\begin{bmatrix}2 & -4 \\ -5 & 7 \\ 2 & 2\end{bmatrix}A=⎣⎡​2−52​−472​⎦⎤​? Explain.

15. What is the solution to $4(y-3)+19=8(2 y+3)+7$ ?

8. Examine the rectangle shown and write down two equations in $x$ and $y$ . Now solve these equations to find the value of $x$ and the value of $y$ .

ion 3.3 Question 8, 3.3.B-6 Part 3 of 8
Find the solution(s) in the set $W$ for each of the following parts a) th A. 7 B. 5 C. 6 D. 8 b) $(11-x)-5=1$ A. 6 - 8 C. 5
0. 7 c) $7+x=x+7$ A. 7

Find the $x$ - and $y$ -intercepts of the graph of $3 x-4 y=27$ . State each answer as an integer or an improper fraction in simplest form.
Answer Attempt 1 out of 2 x-intercept: $\square$ y-intercept: $\square$

Find the slope and the $y$ -intercept of the line. 17) $y=-7 x-6$

Solve the following system of equations. $\begin{array}{l} \frac{1}{6} x-\frac{1}{3} y=-4 \\ \frac{1}{4} x+\frac{3}{5} y=5 \end{array}$ $\begin{array}{l} x=\square \\ y=\square \end{array}$

Use the distributive property to find an equivalent expression: $6(4+2 t)=$ $\square$
DO NOT USE ANY SPACES BETWEEN THE NUMBERS OR OPERATION S

Find an equivalent expression (use the "reverse" method) DO NOT TYPE SPACES $8 u+32=$

Find an equivalent expression (use the "reverse" method) DO NOT TYPE SPACES $8 u+32=$

$\begin{array}{c}\left\{\begin{array}{l}2 x+5 y-27=0 \\ -2 x+27=5 y\end{array}\right. \\ (x, y)=(\square)\end{array}$

15. For a summer landscaping job Jalen makes $\$ 17$ per hour plus a bonus of $\$ 1.50$ for each lawn that he cuts. How much would Jalen make if he cuts 36 lawns while working 42 hours in one week? Create an equation and then solve the problem.

Work the problem and type the correct answer into the box below. (round answer to one decimal place) $\begin{array}{l} 15.3+x=17.7 \\ x=\square \end{array}$

Solve the equation: $-11 x+6-5(x-1)=-5 x-(10 x-4)+5$ . Is it an identity, contradiction, or find the solution set?

Solve the equation using addition and multiplication principles:
$5[7-5(6-r)]-7=7[5(7 r-6)+4]-50$
What is the solution? A. $r=\square$ , B. all real numbers, C. no solution.

Solve the inequalities $8-3x>5$ and $x-5 \geq 10$ , then sketch the solution.

Solve the compound inequality and graph the solution: $3x - 9 > 0$ and $-4x + 9 < 5$ . Provide the solution in interval notation.

Solve the equation: $\frac{3 x+23}{7}+\frac{x+36}{5}=13$ . Provide an integer or simplified fraction as the solution.

Solve: $-7<\frac{4 x-5}{6}<2$ . Choose A, B, C, D, E, or F for the solution set.

Solve the inequality $-3<\frac{4 x-5}{6}<1$ and choose the correct solution set.

Solve the compound inequality: $-17 < 2y - 3 \leq 3$ .

Solve the compound inequality $-17 < 2y - 3 \leq 3$ and express the solution in interval notation. Use decimal values.

Solve the compound inequality $-41 < 4n - 1 \leq 31$ and graph the solution set.

Graph the solution for the inequality $x \geq 5$ .

Solve the inequality $6z - 26.4 < -22 + 5z$ and express the solution in interval notation using decimals.

Solve the inequality $6z - 26.4 < -22 + 5z$ and graph the solution set.

Solve the inequality $6x - 13.2 < -11 + 5x$ and graph the solution set.

Find $\mathbf{u}+\mathbf{v}$ and $\mathbf{u}-3 \mathbf{v}$ for $u=\begin{bmatrix}-3 \\ 6\end{bmatrix}, v=\begin{bmatrix}-5 \\ 4\end{bmatrix}$ .

Find $\mathbf{u}+\mathbf{v}$ and $\mathbf{u}-3 \mathbf{v}$ for $u=\begin{bmatrix}-3 \\ 6\end{bmatrix}$ and $v=\begin{bmatrix}-5 \\ 4\end{bmatrix}$ .

Is vector $b$ a linear combination of $a_{1}, a_{2}, a_{3}$ ? Choose A, B, C, or D based on the echelon matrix pivots.

Is the vector $u=\begin{bmatrix}-7 \\ 10 \\ 8\end{bmatrix}$ in the plane spanned by the columns of $A=\begin{bmatrix}2 & -4 \\ -5 & 7 \\ 2 & 2\end{bmatrix}$ ? Explain.

Solve the inequality: $-7(x-5)>3x-5$ . Provide the solution set in interval notation and graph form.

Solve the compound inequality: $x-3 \leq 6$ and $x+1 \geq 5$ . Provide the solution in interval and graph forms.

Solve the equation: $2(9r + 17) = 16r + 6$ . Fill in the blanks and simplify each step.

Find a number $x$ such that $\frac{1}{4}x + 10 \geq 3$ . What is the solution set in interval notation?

Solve the equation: $3x - 5 = 7x + 11$ . What is the solution set? Choose A, B, or C.

Solve the equation: $0.95 x - 0.99 = 12.93 - 3.85 x$ . What is $x$ ? A. $x=\square$ , B. all real numbers, C. no solution.

Create an equation for this: 19 minus $\frac{5}{3}$ of a number equals 4. Solve for $x$ . Options: A. $19-\frac{5}{3} x=4$ B. $\frac{5}{3}-19 x=4$ C. $19-\frac{5}{3}=4$ D. $5 \frac{5}{3} x-19=4$ . Find $x$ .

Solve the inequality $4z - 9.6 < -7.2 + 3z$ and express the solution in interval notation using decimals.

Solve for $p$ in the equation: $-15 p - 4(6 - 6 p) = 6(p - 3) - 3$ . What is the solution set? A, B, or C?

Solve the inequality $-4 \leq -2x + 2 < 10$ and express the solution in interval notation.

Solve the compound inequality: $-2x < -6$ and $x - 2 < 8$ . What is the solution? A. $x<$ B. $x>$ C. All real numbers. D. No solution.

Find angles A and B where $A + B = 90^{\circ}$ and $A = 2B + 24^{\circ}$ . What are the measures of A and B?

Solve the equation: $2(9r + 17) = 16r + 6$ . Fill in the missing terms and simplify fractions.

Solve the equation: $\frac{2}{7}(5 x+4)=\frac{1}{2}(3 x-26)+12$ . What is $x$ ? A. $x=\square$ B. All real numbers. C. No solution.

Solve the compound inequality $x<2$ or $x<5$ and graph $x<2$ . Choose the correct graph from options A, B, C, or D.

Solve the compound inequality $x+1>6$ or $4-x>5$ . Provide the solution set in interval and graph forms.

Solve the equation step-by-step, filling in missing terms and simplifying fractions:
$7(4b + 2) + 17b = 14$
Find $b$ after applying the distributive property and combining like terms.

Solve the equation step by step. Fill in the blanks and simplify.
$\begin{aligned} -2(-19 w-14) & =-10 \\ \square+28 & =-10 \\ 38 w & = \\ w & = \end{aligned}$

Solve for $y$ in the equation: $3y + 15 - 7 = 14$ .

Solve the equation step by step and fill in the missing terms. Simplify fractions where needed.
$6(13 w+2)-10=2$
$\square+12-10=2$
$78 w+\square=2$
Find $w$ by applying the distributive property and combining like terms.

Solve the equation and fill in the missing terms:
$3y + 15 - 7 = 14$
Complete:
$3y + \square = 14$
$3y = \square$
$y = \square$

Solve the equation: $-5(-2x-17)=-5$ . Find $x$ and simplify.

Solve the equation: $-2c + 2 + 11 = 11$ . Find $c$ after simplifying.

Solve the equation: $7(8 s+1) =s+7$ . Fill in missing terms and simplify to find $s =$ .

Solve the compound inequality: $3(x-4)<15$ or $x+10>14$ . What are the solution options?

Solve the equation: -6b + 6 = -2b + 6. Find missing values and simplify. $-4b = \square, \; b = \square$ .