Browse Algebra problems in the Studdy Learning Bank!

Problem 301

Solve the linear equation $25n + 13 = -27$ for the unknown variable $n$ .

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Problem 302

Solve for $y$ in the equation $4=\frac{y+2}{3}$ .

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Problem 303

Solve for $w$ in the equation $4.5 = 1.5w$ , then check your solution.

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Problem 304

Determine if the linear function $f(x) = 2 - 9x$ is increasing, decreasing, or constant.

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Problem 305

Find the values of $x$ that satisfy $|x-3|=6$ .

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Problem 306

Solve the exponential equation $3^{x}=81$ .

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Problem 307

Solve the linear equation $-\frac{3}{4} z + 1 = -40$ for the variable $z$ .

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Problem 308

Find the value of $y$ when $x=1$ in the equation $y=-3x+2.5$ .

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Problem 309

Find the equation of the line passing through the points $(6, 20)$ and $(8, 42)$ .

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Problem 310

Evaluate the quadratic expression $a^{2} + 5a + 1$ when $a = -4$ .

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Problem 311

Solve for $x$ using addition and multiplication principles, given $-\frac{7}{3} x+\frac{1}{3}=-9$ .

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Problem 312

Eliminate x-terms in system: $3x+5y=5$ , multiply by ? on both sides; $-2x-8y=-6$ , multiply by ? on both sides.

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Problem 313

How many times is $8 \times 10^{5}$ larger than $4 \times 10^{3}$ ? 2,000

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Problem 314

Find the issue with the equation $4+(10 / 5)=6-2$ . The correct answer is (C) The two sides do not evaluate to the same value.

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Problem 315

Find the rational numbers in the set $\left\{-\frac{15}{7},-\sqrt{2}, \sqrt{1}, \sqrt{\frac{4}{9}}, 1, \sqrt{3}, 3.25\right\}$ .

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Problem 316

Find the value of $x$ that satisfies the equation $x-12=-4$ .

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Problem 317

Solve for $f$ where $f+2 \geq 6$ .

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Problem 318

Evaluate the expression $3 \cdot 5^{x}$ when $x = 2$ .

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Problem 319

Solve the linear equation $3x + 7y = 15$ for either $x$ or $y$ .

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Problem 320

Solve for $x$ in the equation $1 + \frac{6}{5x} = 3$ .

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Problem 321

Find the linear equation $y = mx + b$ describing a baby's weight, where the baby weighs 7 lbs at birth and gains 5 lbs every 2 months.

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Problem 322

Solve for $u$ in the equation $-6 u-28=-2(u-6)$ . Simplify the solution.

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Problem 323

Find the correct number line for the expression $-3-1.5$ .

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Problem 324

Find the value of $x$ if the numbers 13, 18, and $x$ have a mean of 18.

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Problem 325

Solve for $x$ when $g(x) = 5x + 2 = 7$ .

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Problem 326

Solve the exponential equations. Verify solutions using graphing technology. a) $4^{3x} = 8^{x-3}$ b) $27^{x} = 9^{2x-3}$ c) $125^{2y-1} = 25^{y+4}$ d) $16^{2k-3} = 32^{k+3}$

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Problem 327

Find the polynomials in standard form. Choose all correct options. $5x^5 + 4x^4 + 12x^3 - 23x + 15$ , $2x^4 - 12x^2 + 5x - 9$ , $5 - 3x$ , $4x^2 + 12x - 13x^3$ .

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Problem 328

Find the value of $d$ given the equation $d^{2}=21$ . Express the solution in simplest radical form.

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Problem 329

Find the equation of the parabola that passes through the points $(3,5), (4,7)$ , and $(5,5)$ .

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Problem 330

Solve absolute value equations: 1) $|4x| = x^2 - 5$ , 2) $2x^2 = |5x + 3|$ , 3) $|2(x-4)^2 - 5| = 3$ , 4) $0 = |x^2 - 2x - 3| - 4$ .

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Problem 331

Solve the linear equation $7(m-12)=5m$ for the value of $m$ .

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Problem 332

Solve for the variable $b$ given the equation $b+a=20$ .

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Problem 333

Solve for the value of $a$ in the equation $-72=8(-7+a)$ .

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Problem 334

Solve for the value of $s$ in the equation $s - 682 = 932$ .

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Problem 335

Find the value of $(k \cdot 61)-211$ for $k=6$ .

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Problem 336

Déterminer l'ensemble de définition de $f(x)=2x^2+x-3$ , $f(x)=\frac{3x}{2x-4}$ , $f(x)=\frac{x^2+3}{x^2-2x}$ , $f(x)=\frac{x^3}{|x|-3}$ .

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Problem 337

Solve the linear equation $16-x=7x$ for the unknown variable $x$ .

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Problem 338

¿Cuál es la razón de cambio de $y$ con respecto a $x$ en la ecuación lineal $y = -5x + 1$ ?

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Problem 339

Find the value of $x$ that satisfies the linear equation $9x + 8 - 2x = -5x - 5 + x$ , rounded to two decimal places.

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Problem 340

Solve the quadratic equation $\frac{1}{2} x^{2}-3 x-\frac{7}{2}=0$ for $x$ .

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Problem 341

Evaluate $5xy + 7x$ when $x=8, y=-6$ .

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Problem 342

Find the number of points $x$ a student needs to score on a 50-point test to get a 78% score. The proportion is $\frac{x}{50} = \frac{78}{100}$ .

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Problem 343

Write an expression for $3x + 4$ using words. Choose the correct phrase: the sum of three times a number and four.

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Problem 344

Solve $vw^2 + y = x$ for $w$ . Given $v=5, x=38, y=-7$ , find $w$ .

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Problem 345

Solve for $x$ in the equation $x=a^{2}x+(a-5)=(a+5)x$ .
Find the indicated sets: (a) $A \cup C$ , (b) $A \cap C$ where $A=\{1,2,3,4,5,6\}$ , $B=\{2,4,6\}$ , and $C=\{6,7,8,9,10\}$ .

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Problem 346

Find the product of the fractions $(x^2 + x)/7$ and $35/(xy + y)$ .

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Problem 347

Find the equation for a number $x$ where 6 less than $x$ is 5.

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Problem 348

Graph the equation $f(x) = -5$ and find the slope.

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Problem 349

Solve the equation $y^{3} + 3y^{2} = 4y + 12$ .

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Problem 350

Solve the equation $1-\frac{3}{2x}=\frac{7}{4}$ and identify it as conditional, inconsistent, or identity.

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Problem 351

Find the solution set to the equation $|3a+5| = |3a-7|$ .

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Problem 352

Evaluate $y = x^{2} - 1$ for $x = -2, -1, 0, 1, 2$ . Plot the $(x, y)$ pairs and graph the function.

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Problem 353

Solve the linear equation $-\frac{4}{3} u=-18$ for the unknown variable $u$ .

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Problem 354

Solve for y given the equation $9=\frac{y}{4}-2$ .

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Problem 355

Solve the quadratic equation $0.0625 x^{2} = 0.125 x + 1.5$ for the value of $x$ .

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Problem 356

Solve for $x$ where $\frac{-5}{x-3}=\frac{-3}{x-1}$ .

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Problem 357

Find $a$ given $b=12$ and $c=11$ using the equation $a=29-b-c$ .

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Problem 358

Solve for $y$ using factoring or the quadratic formula: $y^{2} - 6y + 7 = 0$

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Problem 359

Solve the quadratic equation $x^{2} + 3 = 19$ and select the correct solution(s).

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Problem 360

Simplify $y^{\frac{7}{4}} / y^{\frac{11}{4}}$ assuming positive variables. Express answer as $A$ or $A/B$ with positive exponents.

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Problem 361

Create a compound inequality using digits 1-9 (at most once each) that is equivalent to $2 \leq x < 4$ . Explain your solution.

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Problem 362

Find the integer solutions to the quadratic equation $(n-7)^{2} = 12$ .

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Problem 363

Write an inequality to show the relationship between $-2$ and $-5$ .

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Problem 364

Find the value of $3(1.5 x + 9)$ .

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Problem 365

Multiply the polynomials $(4x+1)$ and $(-3x+5)$ .

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Problem 366

Solve the linear equation $6(a + 3.9) = 19.56$ using a different method. Show the steps.

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Problem 367

Calculate the value of $\frac{x}{4}-2$ when $x=20$

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Problem 368

Find all values of $a_0$ that satisfy the equation $|2a-15| = 7$ .

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Problem 369

Solve the linear equation $\frac{2}{3} a x + 3 = \frac{8}{3} x + 9 b$ for constants $a$ and $b$ . Find the value of $\frac{a}{b}$ if the equation has infinitely many solutions.

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Problem 370

Simplify given expressions. Click "Cannot be simplified" if applicable. $\frac{2y-5}{5-2y}=\square$ and $\frac{-6+y}{y-6}=\square$

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Problem 371

Find the value of $x$ if $9 = 4x$ .

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Problem 372

Find the value of $k$ that satisfies the equation $k-19=45$ .

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Problem 373

Solve for the roots of $3x^2 - 60x + 741 = 0$ using the completing the square method.

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Problem 374

If $f(x)=6x+7$ , find the value of $\nabla$ when $x$ increases by 1 unit.

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Problem 375

Solve for the value of $x$ in the linear equation $x+11=18$ .

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Problem 376

Solve the absolute value inequality $|x-7|>3$ , which represents the set of all real numbers $x$ whose distance from 7 is greater than 3.

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Problem 377

Find the values of $x$ where the equations $y = x^2 - 24$ and $y = x - 12$ intersect.

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Problem 378

Simplify the expression $\frac{x^{2}+5 x-36}{x^{2}-8 x+16}$ and determine which of the following statements are true: 1) It could represent the difference of $\frac{x}{x-4}$ and $\frac{-9}{x-4}$ . 2) It could represent the product of $\frac{x+9}{(x-4)^{2}}$ and $(x-4)$ . 3) It could represent the sum of $\frac{a^{2}+5 a}{x^{2}-8 x}$ and $\frac{-36}{16}$ . 4) It could represent the quotient of $(x-9)$ and $(x-4)$ . 5) It is equivalent to the rational expression $\frac{x+9}{x-4}$ .

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Problem 379

Find the values of y that satisfy the equation $y^{2}=64$ .

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Problem 380

Solve the quadratic equation $y^2 - 2y = 12$ by completing the square. Enter the solutions separated by commas, or "DNE" if no real solution exists.

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Problem 381

Solve for $w$ in the equation $12=2 w+5(w+8)$ . Simplify the solution $w$ .

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Problem 382

Solve $5.14x + 2.25 > 15.1$ . Express the solution as a rational number in decimal form to the tenths place, with $x$ first.

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Problem 383

Solve for $p$ using the square root property: $(3p+2)^2 = 8$ .

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Problem 384

Find the values of $x$ where the function $f(x)=\frac{1}{(x-3)(x-4)}$ is not defined and discontinuous.

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Problem 385

Solve for $y$ in the inequality $4x + 3y \geq 12$ .

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Problem 386

Find the largest value of $x$ that satisfies the equation $\frac{4}{x} = 3 - \frac{1}{2}x$ . (Answer: 2)

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Problem 387

Solve for $Q$ and $R$ where $\frac{R}{D}$ is a proper fraction with $\deg(R) < \deg(D)$ . Also, evaluate $\frac{t^{2}+11 t+24}{t+8}$ .

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Problem 388

Order the expressions using <, >, or = to compare $\left(\frac{1}{9}\right)^{-1}$ , $9^{-2}$ , $9^{-1}$ , and $\left(\frac{1}{9}\right)^{-2}$ .

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Problem 389

Evaluate $g(4)$ for $f(x)=5x^2-3$ and $g(x)=-x+5$ .

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Problem 390

Solve the linear equation $-\frac{1}{2}(12 v-20)+4=-12-8 v$ for the variable $v$ .

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Problem 391

Determine if the degree of the polynomial $f(x) = (x-2)(x-4)(x+1)$ is odd, even, or neither.

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Problem 392

Find the values of the variables $d$ , $e$ , and $f$ that make the given equations true: $\left(2^{d}\right)^{4}=2^{12}$ , $3^{5} \cdot 7^{5}=e^{5}$ , and $5^{0} \cdot 5^{f}=5^{4}$ .

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Problem 393

Find the intersection point of the linear equations $y = -6x + 2$ and $y = 3x - 7$ .

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Problem 394

Find the missing value in the equation $12x + \square = 4(3x + 3)$ .

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Problem 395

Find the value of $2^3 = 8$ .

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Problem 396

Solve the equation $3a - 3 = 6a$ . Select the correct choice: A. $a = \frac{3}{3}$ , B. The solution is all real numbers, C. There is no solution.

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Problem 397

Simplify the product of $\sqrt{18}$ and $\sqrt{63}$ .

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Problem 398

Solve $2y^2 - 96 = 0$ for real $y$ . Round your answer(s) to the nearest hundredth. If there is more than one solution, list them separated by commas. If there is no solution, click "No solution".

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Problem 399

Which equation is nonlinear? $y=x^{2}-4$ or $3y-5x=11$ ?

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Problem 400

Solve the equation $-5=(x+7)^{\frac{1}{2}}-11$ for the value of $x$ .

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Algebra

Problem 301

Solve the linear equation 25n+13=−2725n + 13 = -2725n+13=−27 for the unknown variable nnn.

Problem 302

Solve for yyy in the equation 4=y+234=\frac{y+2}{3}4=3y+2​.

Problem 303

Solve for www in the equation 4.5=1.5w4.5 = 1.5w4.5=1.5w, then check your solution.

Problem 304

Determine if the linear function f(x)=2−9xf(x) = 2 - 9xf(x)=2−9x is increasing, decreasing, or constant.

Problem 305

Find the values of xxx that satisfy ∣x−3∣=6|x-3|=6∣x−3∣=6.

Problem 306

Solve the exponential equation 3x=813^{x}=813x=81.

Problem 307

Solve the linear equation −34z+1=−40-\frac{3}{4} z + 1 = -40−43​z+1=−40 for the variable zzz.

Problem 308

Find the value of yyy when x=1x=1x=1 in the equation y=−3x+2.5y=-3x+2.5y=−3x+2.5.

Problem 309

Find the equation of the line passing through the points (6,20)(6, 20)(6,20) and (8,42)(8, 42)(8,42).

Problem 310

Evaluate the quadratic expression a2+5a+1a^{2} + 5a + 1a2+5a+1 when a=−4a = -4a=−4.

Problem 311

Solve for xxx using addition and multiplication principles, given −73x+13=−9-\frac{7}{3} x+\frac{1}{3}=-9−37​x+31​=−9.

Problem 312

Eliminate x-terms in system: 3x+5y=53x+5y=53x+5y=5, multiply by ? on both sides; −2x−8y=−6-2x-8y=-6−2x−8y=−6, multiply by ? on both sides.

Problem 313

How many times is 8×1058 \times 10^{5}8×105 larger than 4×1034 \times 10^{3}4×103? 2,000

Problem 314

Find the issue with the equation 4+(10/5)=6−24+(10 / 5)=6-24+(10/5)=6−2. The correct answer is (C) The two sides do not evaluate to the same value.

Problem 315

Find the rational numbers in the set {−157,−2,1,49,1,3,3.25}\left\{-\frac{15}{7},-\sqrt{2}, \sqrt{1}, \sqrt{\frac{4}{9}}, 1, \sqrt{3}, 3.25\right\}{−715​,−2​,1​,94​​,1,3​,3.25}.

Problem 316

Find the value of xxx that satisfies the equation x−12=−4x-12=-4x−12=−4.

Problem 317

Solve for fff where f+2≥6f+2 \geq 6f+2≥6.

Problem 318

Evaluate the expression 3⋅5x3 \cdot 5^{x}3⋅5x when x=2x = 2x=2.

Problem 319

Solve the linear equation 3x+7y=153x + 7y = 153x+7y=15 for either xxx or yyy.

Problem 320

Solve for xxx in the equation 1+65x=31 + \frac{6}{5x} = 31+5x6​=3.

Problem 321

Find the linear equation y=mx+by = mx + by=mx+b describing a baby's weight, where the baby weighs 7 lbs at birth and gains 5 lbs every 2 months.

Problem 322

Solve for uuu in the equation −6u−28=−2(u−6)-6 u-28=-2(u-6)−6u−28=−2(u−6). Simplify the solution.

Problem 323

Find the correct number line for the expression −3−1.5-3-1.5−3−1.5.

Problem 324

Find the value of xxx if the numbers 13, 18, and xxx have a mean of 18.

Problem 325

Solve for xxx when g(x)=5x+2=7g(x) = 5x + 2 = 7g(x)=5x+2=7.

Problem 326

Solve the exponential equations. Verify solutions using graphing technology. a) 43x=8x−34^{3x} = 8^{x-3}43x=8x−3 b) 27x=92x−327^{x} = 9^{2x-3}27x=92x−3 c) 1252y−1=25y+4125^{2y-1} = 25^{y+4}1252y−1=25y+4 d) 162k−3=32k+316^{2k-3} = 32^{k+3}162k−3=32k+3

Problem 327

Find the polynomials in standard form. Choose all correct options. 5x5+4x4+12x3−23x+155x^5 + 4x^4 + 12x^3 - 23x + 155x5+4x4+12x3−23x+15, 2x4−12x2+5x−92x^4 - 12x^2 + 5x - 92x4−12x2+5x−9, 5−3x5 - 3x5−3x, 4x2+12x−13x34x^2 + 12x - 13x^34x2+12x−13x3.

Problem 328

Find the value of ddd given the equation d2=21d^{2}=21d2=21. Express the solution in simplest radical form.

Problem 329

Find the equation of the parabola that passes through the points (3,5),(4,7)(3,5), (4,7)(3,5),(4,7), and (5,5)(5,5)(5,5).

Problem 330

Solve absolute value equations: 1) ∣4x∣=x2−5|4x| = x^2 - 5∣4x∣=x2−5, 2) 2x2=∣5x+3∣2x^2 = |5x + 3|2x2=∣5x+3∣, 3) ∣2(x−4)2−5∣=3|2(x-4)^2 - 5| = 3∣2(x−4)2−5∣=3, 4) 0=∣x2−2x−3∣−40 = |x^2 - 2x - 3| - 40=∣x2−2x−3∣−4.

Problem 331

Solve the linear equation 7(m−12)=5m7(m-12)=5m7(m−12)=5m for the value of mmm.

Problem 332

Solve for the variable bbb given the equation b+a=20b+a=20b+a=20.

Problem 333

Solve for the value of aaa in the equation −72=8(−7+a)-72=8(-7+a)−72=8(−7+a).

Problem 334

Solve for the value of sss in the equation s−682=932s - 682 = 932s−682=932.

Problem 335

Find the value of (k⋅61)−211(k \cdot 61)-211(k⋅61)−211 for k=6k=6k=6.

Problem 336

Déterminer l'ensemble de définition de f(x)=2x2+x−3f(x)=2x^2+x-3f(x)=2x2+x−3, f(x)=3x2x−4f(x)=\frac{3x}{2x-4}f(x)=2x−43x​, f(x)=x2+3x2−2xf(x)=\frac{x^2+3}{x^2-2x}f(x)=x2−2xx2+3​, f(x)=x3∣x∣−3f(x)=\frac{x^3}{|x|-3}f(x)=∣x∣−3x3​.

Problem 337

Solve the linear equation 16−x=7x16-x=7x16−x=7x for the unknown variable xxx.

Problem 338

¿Cuál es la razón de cambio de yyy con respecto a xxx en la ecuación lineal y=−5x+1y = -5x + 1y=−5x+1?

Problem 339

Find the value of xxx that satisfies the linear equation 9x+8−2x=−5x−5+x9x + 8 - 2x = -5x - 5 + x9x+8−2x=−5x−5+x, rounded to two decimal places.

Problem 340

Solve the linear equation $25n + 13 = -27$ for the unknown variable $n$ .

Solve for $y$ in the equation $4=\frac{y+2}{3}$ .

Solve for $w$ in the equation $4.5 = 1.5w$ , then check your solution.

Determine if the linear function $f(x) = 2 - 9x$ is increasing, decreasing, or constant.

Find the values of $x$ that satisfy $|x-3|=6$ .

Solve the exponential equation $3^{x}=81$ .

Solve the linear equation $-\frac{3}{4} z + 1 = -40$ for the variable $z$ .

Find the value of $y$ when $x=1$ in the equation $y=-3x+2.5$ .

Find the equation of the line passing through the points $(6, 20)$ and $(8, 42)$ .

Evaluate the quadratic expression $a^{2} + 5a + 1$ when $a = -4$ .

Solve for $x$ using addition and multiplication principles, given $-\frac{7}{3} x+\frac{1}{3}=-9$ .

Eliminate x-terms in system: $3x+5y=5$ , multiply by ? on both sides; $-2x-8y=-6$ , multiply by ? on both sides.

How many times is $8 \times 10^{5}$ larger than $4 \times 10^{3}$ ? 2,000

Find the issue with the equation $4+(10 / 5)=6-2$ . The correct answer is (C) The two sides do not evaluate to the same value.

Find the rational numbers in the set $\left\{-\frac{15}{7},-\sqrt{2}, \sqrt{1}, \sqrt{\frac{4}{9}}, 1, \sqrt{3}, 3.25\right\}$ .

Find the value of $x$ that satisfies the equation $x-12=-4$ .

Solve for $f$ where $f+2 \geq 6$ .

Evaluate the expression $3 \cdot 5^{x}$ when $x = 2$ .

Solve the linear equation $3x + 7y = 15$ for either $x$ or $y$ .

Solve for $x$ in the equation $1 + \frac{6}{5x} = 3$ .

Find the linear equation $y = mx + b$ describing a baby's weight, where the baby weighs 7 lbs at birth and gains 5 lbs every 2 months.

Solve for $u$ in the equation $-6 u-28=-2(u-6)$ . Simplify the solution.

Find the correct number line for the expression $-3-1.5$ .

Find the value of $x$ if the numbers 13, 18, and $x$ have a mean of 18.

Solve for $x$ when $g(x) = 5x + 2 = 7$ .

Solve the exponential equations. Verify solutions using graphing technology. a) $4^{3x} = 8^{x-3}$ b) $27^{x} = 9^{2x-3}$ c) $125^{2y-1} = 25^{y+4}$ d) $16^{2k-3} = 32^{k+3}$

Find the polynomials in standard form. Choose all correct options. $5x^5 + 4x^4 + 12x^3 - 23x + 15$ , $2x^4 - 12x^2 + 5x - 9$ , $5 - 3x$ , $4x^2 + 12x - 13x^3$ .

Find the value of $d$ given the equation $d^{2}=21$ . Express the solution in simplest radical form.

Find the equation of the parabola that passes through the points $(3,5), (4,7)$ , and $(5,5)$ .

Solve absolute value equations: 1) $|4x| = x^2 - 5$ , 2) $2x^2 = |5x + 3|$ , 3) $|2(x-4)^2 - 5| = 3$ , 4) $0 = |x^2 - 2x - 3| - 4$ .

Solve the linear equation $7(m-12)=5m$ for the value of $m$ .

Solve for the variable $b$ given the equation $b+a=20$ .

Solve for the value of $a$ in the equation $-72=8(-7+a)$ .

Solve for the value of $s$ in the equation $s - 682 = 932$ .

Find the value of $(k \cdot 61)-211$ for $k=6$ .

Déterminer l'ensemble de définition de $f(x)=2x^2+x-3$ , $f(x)=\frac{3x}{2x-4}$ , $f(x)=\frac{x^2+3}{x^2-2x}$ , $f(x)=\frac{x^3}{|x|-3}$ .

Solve the linear equation $16-x=7x$ for the unknown variable $x$ .

¿Cuál es la razón de cambio de $y$ con respecto a $x$ en la ecuación lineal $y = -5x + 1$ ?

Find the value of $x$ that satisfies the linear equation $9x + 8 - 2x = -5x - 5 + x$ , rounded to two decimal places.

Solve the quadratic equation $\frac{1}{2} x^{2}-3 x-\frac{7}{2}=0$ for $x$ .

Evaluate $5xy + 7x$ when $x=8, y=-6$ .

Find the number of points $x$ a student needs to score on a 50-point test to get a 78% score. The proportion is $\frac{x}{50} = \frac{78}{100}$ .

Write an expression for $3x + 4$ using words. Choose the correct phrase: the sum of three times a number and four.

Solve $vw^2 + y = x$ for $w$ . Given $v=5, x=38, y=-7$ , find $w$ .

Solve for $x$ in the equation $x=a^{2}x+(a-5)=(a+5)x$ .
Find the indicated sets: (a) $A \cup C$ , (b) $A \cap C$ where $A=\{1,2,3,4,5,6\}$ , $B=\{2,4,6\}$ , and $C=\{6,7,8,9,10\}$ .

Find the product of the fractions $(x^2 + x)/7$ and $35/(xy + y)$ .

Find the equation for a number $x$ where 6 less than $x$ is 5.

Graph the equation $f(x) = -5$ and find the slope.

Solve the equation $y^{3} + 3y^{2} = 4y + 12$ .

Solve the equation $1-\frac{3}{2x}=\frac{7}{4}$ and identify it as conditional, inconsistent, or identity.

Find the solution set to the equation $|3a+5| = |3a-7|$ .

Evaluate $y = x^{2} - 1$ for $x = -2, -1, 0, 1, 2$ . Plot the $(x, y)$ pairs and graph the function.

Solve the linear equation $-\frac{4}{3} u=-18$ for the unknown variable $u$ .

Solve for y given the equation $9=\frac{y}{4}-2$ .

Solve the quadratic equation $0.0625 x^{2} = 0.125 x + 1.5$ for the value of $x$ .

Solve for $x$ where $\frac{-5}{x-3}=\frac{-3}{x-1}$ .

Find $a$ given $b=12$ and $c=11$ using the equation $a=29-b-c$ .

Solve for $y$ using factoring or the quadratic formula: $y^{2} - 6y + 7 = 0$

Solve the quadratic equation $x^{2} + 3 = 19$ and select the correct solution(s).

Simplify $y^{\frac{7}{4}} / y^{\frac{11}{4}}$ assuming positive variables. Express answer as $A$ or $A/B$ with positive exponents.

Create a compound inequality using digits 1-9 (at most once each) that is equivalent to $2 \leq x < 4$ . Explain your solution.

Find the integer solutions to the quadratic equation $(n-7)^{2} = 12$ .

Write an inequality to show the relationship between $-2$ and $-5$ .

Find the value of $3(1.5 x + 9)$ .

Multiply the polynomials $(4x+1)$ and $(-3x+5)$ .

Solve the linear equation $6(a + 3.9) = 19.56$ using a different method. Show the steps.

Calculate the value of $\frac{x}{4}-2$ when $x=20$

Find all values of $a_0$ that satisfy the equation $|2a-15| = 7$ .

Solve the linear equation $\frac{2}{3} a x + 3 = \frac{8}{3} x + 9 b$ for constants $a$ and $b$ . Find the value of $\frac{a}{b}$ if the equation has infinitely many solutions.

Simplify given expressions. Click "Cannot be simplified" if applicable. $\frac{2y-5}{5-2y}=\square$ and $\frac{-6+y}{y-6}=\square$

Find the value of $x$ if $9 = 4x$ .

Find the value of $k$ that satisfies the equation $k-19=45$ .

Solve for the roots of $3x^2 - 60x + 741 = 0$ using the completing the square method.

If $f(x)=6x+7$ , find the value of $\nabla$ when $x$ increases by 1 unit.