$(-\infty, -\dfrac{1}{3}] \cup [\dfrac{13}{6}, \infty)$

Question 1

A chemist is preparing a solution and needs to solve for $x$ in the equation $9x - 5 = 7 + 4x$. What is the value of $x$?

Accepted Answer

$x = \dfrac{12}{5}$

Question 2

A company is comparing two pricing models given by $3(7x - 5) - (6x - 9) = 5x + 12$. What is the solution for $x$?

Accepted Answer

$x = \dfrac{19}{10}$

Question 3

Solve for $x$ in the equation $2x(x + 3) = 3(x^2 + 2x)$, which models the intersection of two parabolic paths.

Accepted Answer

$x = 0$ or $x = 9$

Question 4

A biologist is modeling population growth with the equation $\dfrac{5}{3x-6} = \dfrac{2}{x-2}$. What is the value of $x$?

Accepted Answer

$x = 4$

Question 5

Simplify the expression $(6 + 5i) - (8 - 6i)$, where $i$ is the imaginary unit.

Accepted Answer

$-2 + 11i$

Question 6

Simplify $\sqrt{8} (\sqrt{3} - \sqrt{7})$ and choose the correct answer.

Accepted Answer

$2\sqrt{6} - 2\sqrt{14}$

Question 7

A physicist is analyzing a complex number calculation: $(-4 + 2i)(4 + 3i)$. What is the simplified result?

Accepted Answer

$-22 + i$

Question 8

Solve for $x$ using the square root property: $6x^2 = 150$

Accepted Answer

$x = \pm 5$

Question 9

Solve the quadratic equation by completing the square: $x^2 + 7x + 4 = 0$

Accepted Answer

$x = -\dfrac{7}{2} \pm \dfrac{\sqrt{33}}{2}$

Question 10

Solve the quadratic equation using the quadratic formula: $x^2 + 2x + 26 = 0$

Accepted Answer

$x = -1 \pm 5i$

Question 11

Solve the equation $4x - 3x^2 = 0$ for $x$.

Accepted Answer

$x = 0$ or $x = 1$

Question 12

Solve the inequality $6x + 5 > 4x + 19$ and express the solution in interval notation.

Accepted Answer

$(7, \infty)$

Question 13

Solve the compound inequality $-5 < 3x + 13 < 34$ and express the solution in interval notation.

Accepted Answer

$(-6, 7)$

Question 14

Solve the absolute value inequality $|6x - 5| \geq 8$ and express the solution in interval notation.

Accepted Answer

$(-\infty, -\dfrac{1}{3}] \cup [\dfrac{13}{6}, \infty)$

Question 15

A business is analyzing profit using the equation $x^2 - 2x + 21 = 0$. What are the solutions for $x$?

Accepted Answer

$x = 1 \pm 4.58i$

Question 16

Solve for $x$ in the equation $(x + 35)^{3/2} = 512$.

Accepted Answer

$x = 93$

Question 17

A medical researcher is modeling the spread of a virus with the equation $x^2 + 7x + 4 = 0$. What is the solution for $x$?

Accepted Answer

$x = -\dfrac{7}{2} \pm \dfrac{\sqrt{33}}{2}$

Question 18

Solve the equation $3x + 7 = 9$ for $x$.

Accepted Answer

$x = 2$

Question 19

Solve the inequality $72 + 4x < 18$ and express the solution in interval notation.

Accepted Answer

$(-\infty, -13.5)$

College Algebra: Solving Equations, Simplifying Expressions, and Solving Inequalities

Study Guide - Practice Questions