Question 1

Which of the following is the correct definition of a linear equation in one variable?

Accepted Answer

An equation that can be written in the form $ax + b = 0$, with $a 
eq 0$.

Question 2

Solve the equation $2x - 3 = 3x + 5$. What is the value of $x$?

Accepted Answer

$x = -8$

Question 3

A rational equation is an equation that contains:

Accepted Answer

Variables in the denominator

Question 4

Solve the rational equation $\frac{2x}{3} = \frac{5}{6}$.

Accepted Answer

$x = \frac{5}{4}$

Question 5

Which of the following is the correct solution to the quadratic equation $x^2 - 4x + 3 = 0$?

Accepted Answer

$x = 1$ and $x = 3$

Question 6

A company’s cost function is $C(x) = 1285x + 24943$. What is the cost when $x = 30$?

Accepted Answer

$C(30) = 38,843$

Question 7

Which of the following is the standard form of a complex number?

Accepted Answer

$a + bi$

Question 8

What is the result of multiplying $(2 + 3i)(1 - 4i)$?

Accepted Answer

$14 - 5i$

Question 9

Solve the quadratic equation $x^2 = 9$ using the square root property.

Accepted Answer

$x = 3$ or $x = -3$

Question 10

Which of the following is the correct quadratic formula for solving $ax^2 + bx + c = 0$?

Accepted Answer

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Question 11

If $x$ is a solution to $\frac{5}{2x} = \frac{3}{4}$, what is the value of $x$?

Accepted Answer

$x = \frac{10}{3}$

Question 12

Which of the following best describes the solution set for the inequality $x > 2$?

Accepted Answer

$(2, \infty)$

Question 13

A ladder is leaning against a building. If the ladder is 35 ft long and the base is 10 ft from the building, how high up the wall does the ladder reach? (Use the Pythagorean Theorem.)

Accepted Answer

$\sqrt{35^2 - 10^2} = \sqrt{1225 - 100} = \sqrt{1125} \approx 33.54$ ft

Question 14

Which of the following is the correct solution to $3x + 5 = 2x - 7$?

Accepted Answer

$x = -12$

Question 15

If $x = 2$ is a solution to the equation $ax + b = 0$, what is the value of $a$ if $b = -6$?

Accepted Answer

$a = 3$

Question 16

Which of the following is the correct result of dividing $\frac{8 - 12i}{5 + 12i}$ and writing the answer in standard form?

Accepted Answer

$\frac{8 - 12i}{5 + 12i} = \frac{-40 - 96}{25 + 144} + \frac{60 - 80}{25 + 144}i = \frac{-40}{169} + \frac{-80}{169}i$

College Algebra Study Guide: Linear, Rational, Quadratic Equations, Complex Numbers, and Inequalities

Study Guide - Practice Questions

Study Guide - Flashcards