Linearity

Problem 3201

Find where the lines $y = -x$ and $y = \frac{2}{5}x - 7$ intersect.

See Solution

Problem 3202

Find the intersection of the lines given by $y=\frac{3}{5} x-1$ and $y=\frac{2}{5} x$ .

See Solution

Problem 3203

Solve the equation $\frac{x+6}{16}=\frac{9}{8}+\frac{x-6}{3}$ and identify the solution set: A, B, or C.

See Solution

Problem 3204

1. Solve and check: $3t + 7 = -8$
2. Solve and check: $8 = 16 + 8n$
3. Solve and check: $-34 = 6m - 4$
4. Solve and check: $9x + 27 = -72$
5. Solve and check: $\frac{y}{5} - 6 = 8$

See Solution

Problem 3205

Taub sent 100 texts for \$5.00. How many texts did she send for \$9.55?

See Solution

Problem 3206

Guadalupe texts 91 words in 14 minutes. How many minutes for 143 words? Find $x$ in the ratio table.

See Solution

Problem 3207

Find three consecutive odd integers where the sum of the first two equals five times the largest plus three.

See Solution

Problem 3208

Find three consecutive odd integers where the sum of the first two equals five times the largest plus three.

See Solution

Problem 3209

Find three consecutive odd integers where the sum of the first two equals five times the third plus three: $x + (x + 2) = 5(x + 4) + 3$ .

See Solution

Problem 3210

13. Ricardo spent half his allowance on supplies, then \ $5.25 on a snack, leaving him with \$22.50. Find his allowance$ a$.
14. Liza earned money caring for a pet, spent \ $1.95 on a drink, \$30 on a concert ticket, \$7.20 on a ring, and has \$38.50 left. Find$ m$.
15. Henry bought dog treats, set aside 10, and gave 15 dogs 4 treats each. Find the total treats $t$ in the package.

See Solution

Problem 3211

A shower uses water at a constant rate. If it uses 2 gallons per minute, find the total gallons for any length of shower.

See Solution

Problem 3212

Micah's adult height is 71 inches, which is one less than twice his height at age 2. Find $h$ , his height at age 2.

See Solution

Problem 3213

Solve for $x$ in each equation, assuming $a \neq 0$ :
1. $4 = a x - 14$
2. $a x - 5 = 19$
3. $6 + a x = -29$
4. $\frac{8}{a x} - 5 = -3$
5. $18 - a x = 42$

See Solution

Problem 3214

Solve the inequality $2y + 6 > 20$ and identify the correct graph of the solution.

See Solution

Problem 3215

Solve the equations and verify your answers:
1. $\frac{5 r}{2}-6=19$
2. $\frac{n}{3}-8=-2$
3. $5+\frac{x}{4}=1$
4. $-\frac{h}{3}-4=13$
5. $5(1+n)=-5$

See Solution

Problem 3216

Liam's class plants bamboo. Write the slope-intercept equation $y=20x+10$ and explain the slope and $y$ -intercept.

See Solution

Problem 3217

Use row operations to solve the system: $7 x_{1} + 14 x_{2} = 7 5 x_{1} + 8 x_{2} = 11$ Find the values of $x_{1}$ and $x_{2}$ .

See Solution

Problem 3218

Do the planes $x_{1}+4 x_{2}+x_{3}=5$ , $x_{2}-x_{3}=1$ , and $x_{1}+5 x_{2}=1$ intersect? Choose A, B, or C.

See Solution

Problem 3219

Identify the error in the following steps:
14x - 3(3x - 3) = 4x + 2 leads to x = 11.
A. Sign error in distribution. B. Addition error in combining terms. C. Addition error when isolating x.

See Solution

Problem 3220

Which expressions equal $4 x$ ? Choose two: (A) $3 x+x$ , (B) $2 x+2$ , (C) $4+x$ , (D) $8 x-4$ .

See Solution

Problem 3221

Find values for the inequality $c+10<17$ . Choose two from: 3, 5, 7, 11, 14.

See Solution

Problem 3222

Identify the error in the solution steps for the equation $14 x-3(3 x-3) =4 x+2$ . What is the correct solution?

See Solution

Problem 3223

Solve the equation: $14 x - 3(3 x - 3) = 4 x + 2$ .

See Solution

Problem 3224

Solve for $x$ in the equation: $6 - 2x = 6x - 10x + 10$ .

See Solution

Problem 3225

Solve for $x$ : $8(x+4)=10(x-2)$

See Solution

Problem 3226

Solve the equation $2(2t-5)=20-2t$ . What is the solution set? A. (Enter integer or fraction) B. All real numbers C. Empty set.

See Solution

Problem 3227

Solve $2x + 17 = 3$ . Is it an identity, contradiction, or what is the solution set? A, B, or C?

See Solution

Problem 3228

Find the general solution of the system from the matrix: $\left[\begin{array}{rrrr} 0 & 1 & -2 & 5 \\ 1 & -4 & 4 & -14 \end{array}\right]$ Choose A, B, C, or D.

See Solution

Problem 3229

Solve the equation: $-4(k+1)-k-13=-5(k+5)+8$ .

See Solution

Problem 3230

Solve the equation: $7[2-(3+2 x)]-2 x=-9+2(1-8 x)$ .

See Solution

Problem 3231

Solve the equation: $5x + 8(x - 6) = 5(x - 8)$ .

See Solution

Problem 3232

Solve the equation: $\frac{5}{6} x - x = \frac{9}{10} x - 5$ .

See Solution

Problem 3233

Choose values for $h$ and $k$ so the system has (a) no solution, (b) a unique solution, (c) many solutions.

See Solution

Problem 3234

Solve for $x$ in the equation: $-0.10(28)+0.35 x=0.05(x-20)$ .

See Solution

Problem 3235

Solve for $x$ in the equation $\frac{x}{2}+\frac{x}{7}=9$ .

See Solution

Problem 3236

Solve for $y$ in the equation $0.15 y + 0.07(y + 5000) = 1670$ .

See Solution

Problem 3237

Mark Adler earns \$1,650 monthly. His new job pays \$9.80/hour with time and a half over 36 hours. How many overtime hours per week are needed to match his current weekly earnings?

See Solution

Problem 3238

Compare the graphs of $y=x$ , $y=x+\frac{5}{6}$ , and $y=-2x$ . Answer questions about steepness and $y$ -intercepts.

See Solution

Problem 3239

Prove that if $-\frac{1}{6} r - 5 = 38$ , then $r = -258$ using a two-column format.

See Solution

Problem 3240

Which teacher's quiz table shows a proportional relationship between the number of questions and point value?

See Solution

Problem 3241

Find the value of $\frac{1}{3}x - \frac{3}{4}$ for $x=\frac{1}{4}$ .

See Solution

Problem 3242

Paul sells \ $2 raffle tickets. To earn a jacket, he needs \$230 total. If he sold \$50, how many more tickets,$ x $, does he need? (A)$ x \geq 90 $(B)$ x \leq 90 $(C)$ x \geq 180 $(D)$ x \leq 180$

See Solution

Problem 3243

Which expression equals $(13 x-4)-(20 x-15)$ ? (A) $33 x+11$ (B) $33 x-19$ (C) $-7 x-19$ (D) $-7 x+11$

See Solution

Problem 3244

Zach's first quiz score is what if his last score is $30$ less than $2$ times his first, and their sum is $150$ ?

See Solution

Problem 3245

Solve these equations for $x$ : 1. $16x = 176$ , 2. $16x = 8$ , 3. $16x = 1$ , 4. $\frac{1}{5}x = 1$ , 5. $\frac{2}{5}x = 1$ .

See Solution

Problem 3246

Becky has dimes equal to Ryan and Amy combined. Ryan has 2 more than Amy, who has one third of Becky's dimes. Find their dimes.

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Problem 3247

A cup of skim milk has 10 more than half the calories of whole milk. Whole milk has 40 more calories than apple juice. Total is 370. Find calories in each.

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Problem 3248

A set of quarters and dimes totals \$6.75. Dimes are 4 less than 3 times quarters. Find the quantities.

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Problem 3249

Solve for $B$ in the equation $\frac{6}{5} B + g^{2} = d$ , considering capitalization.

See Solution

Problem 3250

Rob's current age if he will be 81 in ten years is given by the equation: $x + 10 = 81$ .

See Solution

Problem 3251

In a library, $40\%$ of books are in English, $80\%$ of the rest are in Hindi, and 240 are in other languages. Total books?

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Problem 3252

The drama club sells student tickets for \ $5.50 and adult tickets for \$9. Max capacity is 140 people, and they need at least \$990. Let$ x $be student tickets and$ y$ adult tickets. Write and solve the inequalities graphically to find one solution.

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Problem 3253

Find the values of $k$ for the inequality $5 < k - 2 < 11$ .

See Solution

Problem 3254

Solve for $y$ in the equation $4y - 12 = 4x$ .

See Solution

Problem 3255

Find the equation equivalent to average velocity $v = \frac{d_{2}-d_{1}}{t_{2}-t_{1}}$ . Options: A, B, C, D.

See Solution

Problem 3256

Solve the equation $2y=2x-20$ for a given value of 'x' or 'y'.

See Solution

Problem 3257

Solve for $x$ in the equation $8 = 16x - 24$ .

See Solution

Problem 3258

Solve for $x$ in the equation $8y = 16x - 24$ .

See Solution

Problem 3259

Solve for $y$ in the equation $8y = 16x - 24$ .

See Solution

Problem 3260

See Solution

Problem 3261

Find an equation for the average speed of an airplane in miles $(M)$ per hour $(h)$ based on its travel data.

See Solution

Problem 3262

Solve for $n$ in the equation: $24=13n-4n+9$ .

See Solution

Problem 3263

Priscilla's patch produces 6 lbs of strawberries for every 12 ft of plants. Find the equation for pounds $(P)$ per feet $(f)$ : $P = 0.5f$

See Solution

Problem 3264

Find the equation for the number of people $n$ each of the 10 cars can hold if 40 people ride at once. Options: $n / 10=40$ , $10 n=40$ , $n+10=40$ , $n-10=40$ .

See Solution

Problem 3265

Solve the system of equations:
1. $2x - y = 7$
2. $x = 2y - 1$
Substitute $x$ into the first equation. What do you get?
Options: a. $2x - y = 2y - 1$ b. $2(2y - 1) - y = 7$ c. $x = 2(2x - y) - 1$ d. $2x - (2y - 1) = 7$

See Solution

Problem 3266

Find the smallest integer $x$ that satisfies the inequality $5x + 4.6 \geq 20.4$ . Options: A. 2 B. 3 C. 4 D. 5 E. 6

See Solution

Problem 3267

Solve the system: $X + Y = 10$ , $Y - X = 8$ . Find the product $X * Y$ .

See Solution

Problem 3268

Jun sells necklaces for \$5.00 each, costing \$0.50 to make. With a \$95 vendor fee, how many must he sell to profit?

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Problem 3269

Identify the system of linear equations that has infinitely many solutions. Choose one: a. $5 x+4 y=-14$ and $3 x+6 y=6$ b. $2 x+8 y=6$ and $-5 x-20 y=-15$ c. $-x-7 y=14$ and $-4 x-14 y=28$ d. $8 x+14 y=4$ and $-6 x-7 y=-10$

See Solution

Problem 3270

Jun sells necklaces for \$5.00, costing \$0.50 each. With a \$95.00 fee, how many must he sell to profit? A. 19 B. 20 C. 21 D. 22 E. 23

See Solution

Problem 3271

Which equation has a solution of $t=5$ ? Choose one: a. $8 t-10+2 t=5 t-35$ b. $2(2 t-4)-2 t=-2$ c. $3 t+10=6 t-5$ d. $2-3(t+4)=2 t+15$

See Solution

Problem 3272

Verify the equation: $[64 + (-40)] + 16 = 64 + [(-40) + 16]$ . Show both sides equal 36.

See Solution

Problem 3273

In a school, $20\%$ are infants under 7. Girls above 7 are $2/3$ of boys above 7, totaling 64. Find total scholars: (a) 200 (b) 250 (c) 320 (d) 270 (e) None.

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Problem 3274

In a school, $20\%$ are infants under 7. Girls above 7 are $2/3$ of boys above 7, totaling 64. Find total scholars: (a) 200 (b) 250 (c) 320 (d) 270 (e) None.

See Solution

Problem 3275

A student scored $25\%$ and failed by 60 marks, while another scored $45\%$ and passed by 10 marks. Find max marks: (a) 450 (b) 350 (c) 525 (d) None of these

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Problem 3276

Rs. 5214 is shared among $A, B,$ and $C$ where $A$ gets $25\%$ more than $B$ and $20\%$ more than $C$ . Find $A$ 's share.

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Problem 3277

Solve the compound inequality: $x+4>8$ or $4-x>6$ . Provide the solution set in interval and graph forms.

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Problem 3278

Solve the compound inequality: $x+3>11$ or $-2x+4 \geq 8$ . Provide the solution in interval and graph form.

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Problem 3279

Solve for $x$ : $2(x+7)+3x=12$ . What is the first step?

See Solution

Problem 3280

Solve the equations: $2x - 4 = 10$ and $2x - 4 = -10$ .

See Solution

Problem 3281

Solve for $b$ in the equation $2(6 b+8)=6 b+4$ .

See Solution

Problem 3282

Find two two-digit numbers with reversed digits. Their difference is 54 and the sum of the digits is 10.

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Problem 3283

Combine the terms: $8y - 9y$ . What is the simplified result?

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Problem 3284

Which algebraic expression represents "8 less than the product of 12 and a number $x$ "? Options: $12x - 8$ , $8 - 12x$ , $12 - 8x$ , $8x - 12$ .

See Solution

Problem 3285

Distribute $-4$ into the expression $7x + 5$ .

See Solution

Problem 3286

Which expression is equivalent to $-5(-6 h+8-12) ?$ $30 h+40+60$ $-30 h+40-60$ $30 h-40+60$ $-30 h-40-60$

See Solution

Problem 3287

$\begin{array}{l} \frac{2}{3} x-\frac{4}{3} y=8 \\ A(3 x-1)=3 y \end{array}$
In the system of equations, $A$ is a constant. For which value of $A$ is there exactly one solution $(x, y)$ where $y=0$ ?

See Solution

Problem 3288

$\begin{aligned} 0.5(8 w+2 v) & =3 \\ 8 w & =2-v+4 w \end{aligned}$
Which of the following accurately describes all solutions to the system of equations shown?
Choose 1 answer: (A) $v=1$ and $w=\frac{1}{4}$ (B) $v=4$ and $w=-\frac{1}{4}$ (c) There are infinite solutions to the system. (D) There are no solutions to the system.

See Solution

Problem 3289

$\begin{array}{l}2.8 y+2.2 y=51 y \\ 5 x+4 x+2 x=11 x\end{array}$

See Solution

Problem 3290

$5 y-13+y$

See Solution

Problem 3291

Maximize $p=5 x-4 y+3 z$ subject to $\begin{array}{c} 2 x+2 z \leq 100 \\ 5 y-5 z \leq 50 \\ 2 x-5 y \leq 50 \\ x \geq 0, y \geq 0, z \geq 0 \end{array}$

See Solution

Problem 3292

Consider the following system of equations and its graph: $\left\{\begin{array}{l} 2 x+y=-1 \\ 4 x-y=7 \end{array}\right.$ A) What is the solution of the system?
Answer: $(x, y)=($ $\square$ $\square$ B) In the boxes below, enter either the letter A or B to match the equation to the graph shown. $\square$ $2 x+y=-1$ a. Graph A $\square$ $4 x-y=7$ b. Graph B

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Problem 3293

$4x + 3y = 9$

See Solution

Problem 3294

Solve the system of equations by graphing: $\left\{\begin{array}{ll} -4 x+y-15= & 0 \\ -1 x+y-3= & 0 \end{array}\right.$
Answer: $(x, y)=($ $\square$ $\square$ )

See Solution

Problem 3295

Solve the following system of equations with the substitution method: $\left\{\begin{array}{ll} x-2 y & =0 \\ y & =-4 x-36 \end{array}\right.$
Answer: $(x, y)=($ $\square$ , $\square$ ) Preview $x$ : Preview $y$ :
Enter your answers as integers or as reduced fractions in the form A/B.

See Solution

Problem 3296

$2x + 5y = 13$

See Solution

Problem 3297

Supply \& Demand In supply (and demand) problems, $y$ is the number of items the supplier will produce (or the public will buy) if the price of the item is $x$ .
For a particular product, the supply equation is $\begin{array}{c} y=4 x+384 \\ y=-8 x+612 \end{array}$
What is the intersection point of these two lines? $\square$ Enter answer as an ordered pair (don't forget the parentheses). What is the selling price when supply and demand are in eqtilibrium? price $=\$$ $\square$ /item
What is the amount of items in the market when supply and demand are in equilibrium? number of items = $\square$

See Solution

Problem 3298

Solve this system of equations $\begin{array}{l} \left\{\begin{array}{l} x+3 y=-4 \\ 3 x+y=4 \end{array}\right. \\ x=\square \\ y=\square \end{array}$

See Solution

Problem 3299

Solve the system of equations by graphing: $\left\{\begin{array}{l} y+7=-5 x \\ y+6 x=-9 \end{array}\right.$ One solution: $\square$ No solution Infinite number of solutions

See Solution

Problem 3300

Tayler has $\$ 320$ to pay for dining room chairs. She expects to pay about $\$ 80$ per chair. Her friend told her that she has 3 that Taylor can have for free.
Complete the equation below to find the total number of chairs that Taylor can get for her dining room. Use $c$ to represent the total chairs. CLEAR CHECK $\square$ ( $\square$ $\square$ $\square$

See Solution

1 ...30 31 32 33 34 35 36 ...61

Linearity

Problem 3201

Find where the lines y=−xy = -xy=−x and y=25x−7y = \frac{2}{5}x - 7y=52​x−7 intersect.

Problem 3202

Find the intersection of the lines given by y=35x−1y=\frac{3}{5} x-1y=53​x−1 and y=25xy=\frac{2}{5} xy=52​x.

Problem 3203

Solve the equation x+616=98+x−63\frac{x+6}{16}=\frac{9}{8}+\frac{x-6}{3}16x+6​=89​+3x−6​ and identify the solution set: A, B, or C.

Problem 3204

1. Solve and check: 3t+7=−83t + 7 = -83t+7=−8 2. Solve and check: 8=16+8n8 = 16 + 8n8=16+8n 3. Solve and check: −34=6m−4-34 = 6m - 4−34=6m−4 4. Solve and check: 9x+27=−729x + 27 = -729x+27=−72 5. Solve and check: y5−6=8\frac{y}{5} - 6 = 85y​−6=8

Problem 3205

Taub sent 100 texts for \$5.00. How many texts did she send for \$9.55?

Problem 3206

Guadalupe texts 91 words in 14 minutes. How many minutes for 143 words? Find xxx in the ratio table.

Problem 3207

Find three consecutive odd integers where the sum of the first two equals five times the largest plus three.

Problem 3208

Find three consecutive odd integers where the sum of the first two equals five times the largest plus three.

Problem 3209

Find three consecutive odd integers where the sum of the first two equals five times the third plus three: x+(x+2)=5(x+4)+3x + (x + 2) = 5(x + 4) + 3x+(x+2)=5(x+4)+3.

Problem 3210

Problem 3211

A shower uses water at a constant rate. If it uses 2 gallons per minute, find the total gallons for any length of shower.

Problem 3212

Micah's adult height is 71 inches, which is one less than twice his height at age 2. Find hhh, his height at age 2.

Problem 3213

Solve for xxx in each equation, assuming a≠0a \neq 0a=0:1. 4=ax−144 = a x - 144=ax−142. ax−5=19a x - 5 = 19ax−5=193. 6+ax=−296 + a x = -296+ax=−294. 8ax−5=−3\frac{8}{a x} - 5 = -3ax8​−5=−35. 18−ax=4218 - a x = 4218−ax=42

Problem 3214

Solve the inequality 2y+6>202y + 6 > 202y+6>20 and identify the correct graph of the solution.

Problem 3215

Solve the equations and verify your answers: 1. 5r2−6=19\frac{5 r}{2}-6=1925r​−6=19 2. n3−8=−2\frac{n}{3}-8=-23n​−8=−2 3. 5+x4=15+\frac{x}{4}=15+4x​=1 4. −h3−4=13-\frac{h}{3}-4=13−3h​−4=13 5. 5(1+n)=−55(1+n)=-55(1+n)=−5

Problem 3216

Liam's class plants bamboo. Write the slope-intercept equation y=20x+10y=20x+10y=20x+10 and explain the slope and yyy-intercept.

Problem 3217

Use row operations to solve the system: 7x1+14x2=75x1+8x2=11 7 x_{1} + 14 x_{2} = 7 5 x_{1} + 8 x_{2} = 11 7x1​+14x2​=75x1​+8x2​=11 Find the values of x1x_{1}x1​ and x2x_{2}x2​.

Problem 3218

Do the planes x1+4x2+x3=5x_{1}+4 x_{2}+x_{3}=5x1​+4x2​+x3​=5, x2−x3=1x_{2}-x_{3}=1x2​−x3​=1, and x1+5x2=1x_{1}+5 x_{2}=1x1​+5x2​=1 intersect? Choose A, B, or C.

Problem 3219

Identify the error in the following steps: 14x - 3(3x - 3) = 4x + 2 leads to x = 11. A. Sign error in distribution. B. Addition error in combining terms. C. Addition error when isolating x.

Problem 3220

Which expressions equal 4x4 x4x? Choose two: (A) 3x+x3 x+x3x+x, (B) 2x+22 x+22x+2, (C) 4+x4+x4+x, (D) 8x−48 x-48x−4.

Problem 3221

Find values for the inequality c+10<17c+10<17c+10<17. Choose two from: 3, 5, 7, 11, 14.

Problem 3222

Identify the error in the solution steps for the equation 14x−3(3x−3)=4x+214 x-3(3 x-3) =4 x+214x−3(3x−3)=4x+2. What is the correct solution?

Problem 3223

Solve the equation: 14x−3(3x−3)=4x+214 x - 3(3 x - 3) = 4 x + 214x−3(3x−3)=4x+2.

Problem 3224

Solve for xxx in the equation: 6−2x=6x−10x+106 - 2x = 6x - 10x + 106−2x=6x−10x+10.

Problem 3225

Solve for xxx: 8(x+4)=10(x−2)8(x+4)=10(x-2)8(x+4)=10(x−2)

Problem 3226

Solve the equation 2(2t−5)=20−2t2(2t-5)=20-2t2(2t−5)=20−2t. What is the solution set? A. (Enter integer or fraction) B. All real numbers C. Empty set.

Problem 3227

Solve 2x+17=32x + 17 = 32x+17=3. Is it an identity, contradiction, or what is the solution set? A, B, or C?

Problem 3228

Find the general solution of the system from the matrix: [01−251−44−14] \left[\begin{array}{rrrr} 0 & 1 & -2 & 5 \\ 1 & -4 & 4 & -14 \end{array}\right] [01​1−4​−24​5−14​] Choose A, B, C, or D.

Problem 3229

Solve the equation: −4(k+1)−k−13=−5(k+5)+8-4(k+1)-k-13=-5(k+5)+8−4(k+1)−k−13=−5(k+5)+8.

Problem 3230

Solve the equation: 7[2−(3+2x)]−2x=−9+2(1−8x)7[2-(3+2 x)]-2 x=-9+2(1-8 x)7[2−(3+2x)]−2x=−9+2(1−8x).

Problem 3231

Solve the equation: 5x+8(x−6)=5(x−8)5x + 8(x - 6) = 5(x - 8)5x+8(x−6)=5(x−8).

Problem 3232

Solve the equation: 56x−x=910x−5\frac{5}{6} x - x = \frac{9}{10} x - 565​x−x=109​x−5.

Problem 3233

Choose values for hhh and kkk so the system has (a) no solution, (b) a unique solution, (c) many solutions.

Problem 3234

Solve for xxx in the equation: −0.10(28)+0.35x=0.05(x−20)-0.10(28)+0.35 x=0.05(x-20)−0.10(28)+0.35x=0.05(x−20).

Problem 3235

Solve for xxx in the equation x2+x7=9\frac{x}{2}+\frac{x}{7}=92x​+7x​=9.

Problem 3236

Solve for yyy in the equation 0.15y+0.07(y+5000)=16700.15 y + 0.07(y + 5000) = 16700.15y+0.07(y+5000)=1670.

Problem 3237

Mark Adler earns \$1,650 monthly. His new job pays \$9.80/hour with time and a half over 36 hours. How many overtime hours per week are needed to match his current weekly earnings?

Problem 3238

Compare the graphs of y=xy=xy=x, y=x+56y=x+\frac{5}{6}y=x+65​, and y=−2xy=-2xy=−2x. Answer questions about steepness and yyy-intercepts.

Problem 3239

Prove that if −16r−5=38-\frac{1}{6} r - 5 = 38−61​r−5=38, then r=−258r = -258r=−258 using a two-column format.

Problem 3240

Which teacher's quiz table shows a proportional relationship between the number of questions and point value?

Find where the lines $y = -x$ and $y = \frac{2}{5}x - 7$ intersect.

Find the intersection of the lines given by $y=\frac{3}{5} x-1$ and $y=\frac{2}{5} x$ .

Solve the equation $\frac{x+6}{16}=\frac{9}{8}+\frac{x-6}{3}$ and identify the solution set: A, B, or C.

1. Solve and check: $3t + 7 = -8$
2. Solve and check: $8 = 16 + 8n$
3. Solve and check: $-34 = 6m - 4$
4. Solve and check: $9x + 27 = -72$
5. Solve and check: $\frac{y}{5} - 6 = 8$

Guadalupe texts 91 words in 14 minutes. How many minutes for 143 words? Find $x$ in the ratio table.

Find three consecutive odd integers where the sum of the first two equals five times the third plus three: $x + (x + 2) = 5(x + 4) + 3$ .

Micah's adult height is 71 inches, which is one less than twice his height at age 2. Find $h$ , his height at age 2.

Solve for $x$ in each equation, assuming $a \neq 0$ :
1. $4 = a x - 14$
2. $a x - 5 = 19$
3. $6 + a x = -29$
4. $\frac{8}{a x} - 5 = -3$
5. $18 - a x = 42$

Solve the inequality $2y + 6 > 20$ and identify the correct graph of the solution.

Solve the equations and verify your answers:
1. $\frac{5 r}{2}-6=19$
2. $\frac{n}{3}-8=-2$
3. $5+\frac{x}{4}=1$
4. $-\frac{h}{3}-4=13$
5. $5(1+n)=-5$

Liam's class plants bamboo. Write the slope-intercept equation $y=20x+10$ and explain the slope and $y$ -intercept.

Use row operations to solve the system: $7 x_{1} + 14 x_{2} = 7 5 x_{1} + 8 x_{2} = 11$ Find the values of $x_{1}$ and $x_{2}$ .

Do the planes $x_{1}+4 x_{2}+x_{3}=5$ , $x_{2}-x_{3}=1$ , and $x_{1}+5 x_{2}=1$ intersect? Choose A, B, or C.

Identify the error in the following steps:
14x - 3(3x - 3) = 4x + 2 leads to x = 11.
A. Sign error in distribution. B. Addition error in combining terms. C. Addition error when isolating x.

Which expressions equal $4 x$ ? Choose two: (A) $3 x+x$ , (B) $2 x+2$ , (C) $4+x$ , (D) $8 x-4$ .

Find values for the inequality $c+10<17$ . Choose two from: 3, 5, 7, 11, 14.

Identify the error in the solution steps for the equation $14 x-3(3 x-3) =4 x+2$ . What is the correct solution?

Solve the equation: $14 x - 3(3 x - 3) = 4 x + 2$ .

Solve for $x$ in the equation: $6 - 2x = 6x - 10x + 10$ .

Solve for $x$ : $8(x+4)=10(x-2)$

Solve the equation $2(2t-5)=20-2t$ . What is the solution set? A. (Enter integer or fraction) B. All real numbers C. Empty set.

Solve $2x + 17 = 3$ . Is it an identity, contradiction, or what is the solution set? A, B, or C?

Find the general solution of the system from the matrix: $\left[\begin{array}{rrrr} 0 & 1 & -2 & 5 \\ 1 & -4 & 4 & -14 \end{array}\right]$ Choose A, B, C, or D.

Solve the equation: $-4(k+1)-k-13=-5(k+5)+8$ .

Solve the equation: $7[2-(3+2 x)]-2 x=-9+2(1-8 x)$ .

Solve the equation: $5x + 8(x - 6) = 5(x - 8)$ .

Solve the equation: $\frac{5}{6} x - x = \frac{9}{10} x - 5$ .

Choose values for $h$ and $k$ so the system has (a) no solution, (b) a unique solution, (c) many solutions.

Solve for $x$ in the equation: $-0.10(28)+0.35 x=0.05(x-20)$ .

Solve for $x$ in the equation $\frac{x}{2}+\frac{x}{7}=9$ .

Solve for $y$ in the equation $0.15 y + 0.07(y + 5000) = 1670$ .

Compare the graphs of $y=x$ , $y=x+\frac{5}{6}$ , and $y=-2x$ . Answer questions about steepness and $y$ -intercepts.

Prove that if $-\frac{1}{6} r - 5 = 38$ , then $r = -258$ using a two-column format.

Find the value of $\frac{1}{3}x - \frac{3}{4}$ for $x=\frac{1}{4}$ .

Which expression equals $(13 x-4)-(20 x-15)$ ? (A) $33 x+11$ (B) $33 x-19$ (C) $-7 x-19$ (D) $-7 x+11$

Zach's first quiz score is what if his last score is $30$ less than $2$ times his first, and their sum is $150$ ?

Solve these equations for $x$ : 1. $16x = 176$ , 2. $16x = 8$ , 3. $16x = 1$ , 4. $\frac{1}{5}x = 1$ , 5. $\frac{2}{5}x = 1$ .

Solve for $B$ in the equation $\frac{6}{5} B + g^{2} = d$ , considering capitalization.

Rob's current age if he will be 81 in ten years is given by the equation: $x + 10 = 81$ .

In a library, $40\%$ of books are in English, $80\%$ of the rest are in Hindi, and 240 are in other languages. Total books?

Find the values of $k$ for the inequality $5 < k - 2 < 11$ .

Solve for $y$ in the equation $4y - 12 = 4x$ .

Find the equation equivalent to average velocity $v = \frac{d_{2}-d_{1}}{t_{2}-t_{1}}$ . Options: A, B, C, D.

Solve the equation $2y=2x-20$ for a given value of 'x' or 'y'.

Solve for $x$ in the equation $8 = 16x - 24$ .

Solve for $x$ in the equation $8y = 16x - 24$ .

Solve for $y$ in the equation $8y = 16x - 24$ .

Find an equation for the average speed of an airplane in miles $(M)$ per hour $(h)$ based on its travel data.

Solve for $n$ in the equation: $24=13n-4n+9$ .

Priscilla's patch produces 6 lbs of strawberries for every 12 ft of plants. Find the equation for pounds $(P)$ per feet $(f)$ : $P = 0.5f$

Find the equation for the number of people $n$ each of the 10 cars can hold if 40 people ride at once. Options: $n / 10=40$ , $10 n=40$ , $n+10=40$ , $n-10=40$ .

Find the smallest integer $x$ that satisfies the inequality $5x + 4.6 \geq 20.4$ . Options: A. 2 B. 3 C. 4 D. 5 E. 6

Solve the system: $X + Y = 10$ , $Y - X = 8$ . Find the product $X * Y$ .

Which equation has a solution of $t=5$ ? Choose one: a. $8 t-10+2 t=5 t-35$ b. $2(2 t-4)-2 t=-2$ c. $3 t+10=6 t-5$ d. $2-3(t+4)=2 t+15$

Verify the equation: $[64 + (-40)] + 16 = 64 + [(-40) + 16]$ . Show both sides equal 36.

In a school, $20\%$ are infants under 7. Girls above 7 are $2/3$ of boys above 7, totaling 64. Find total scholars: (a) 200 (b) 250 (c) 320 (d) 270 (e) None.

In a school, $20\%$ are infants under 7. Girls above 7 are $2/3$ of boys above 7, totaling 64. Find total scholars: (a) 200 (b) 250 (c) 320 (d) 270 (e) None.