Question 1

Which of the following is the correct solution to the linear equation $2x + 3 = 11$?

Accepted Answer

$x = 4$

Question 2

Solve the equation $\frac{1}{2}(x + 2) = \frac{3}{4}$ for $x$.

Accepted Answer

$x = -0.5$

Question 3

Which of the following equations is an identity?

Accepted Answer

$2(x + 5) = 2x + 10$

Question 4

Simplify $i^{23}$, where $i$ is the imaginary unit.

Accepted Answer

$i$

Question 5

What is the standard form of the complex number $2 - 3i$?

Accepted Answer

$2 - 3i$

Question 6

Find the product of $(3 + 2i)(4 - i)$ and express your answer in standard form.

Accepted Answer

$14 + 5i$

Question 7

If $a = 2$ and $b = -5$, what is the conjugate of the complex number $a + bi$?

Accepted Answer

$2 - 5i$

Question 8

Divide $\frac{3}{1 + 2i}$ and express your answer in standard form.

Accepted Answer

$\frac{3}{1 + 2i} = \frac{3(1 - 2i)}{(1 + 2i)(1 - 2i)} = \frac{3 - 6i}{1 + 4} = \frac{3 - 6i}{5} = 0.6 - 1.2i$

Question 9

Which of the following is the correct quadratic equation in standard form for $2x - 6 = 0$?

Accepted Answer

$ax^2 + bx + c = 0$

Question 10

Solve the quadratic equation $x^2 + 4x + 4 = 0$ by factoring.

Accepted Answer

$x = -2$

Question 11

Using the quadratic formula, solve $x^2 - 5x + 6 = 0$.

Accepted Answer

$x = 2$ and $x = 3$

Question 12

Determine the number and type of solutions for the quadratic equation $x^2 + 4x + 5 = 0$ using the discriminant.

Accepted Answer

Two imaginary solutions

Question 13

Express the solution set of $x + 3 \leq 5$ in interval notation.

Accepted Answer

$(-\infty, 2]$

Question 14

Solve the inequality $2x + 12 > 19$ and express the solution in interval notation.

Accepted Answer

$(3.5, \infty)$

Question 15

Which of the following is a rational equation?

Accepted Answer

$\frac{1}{x} = 12$

Question 16

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

Question 17

Which interval notation represents the solution set for $x > -3$?

Accepted Answer

$(-3, \infty)$

Question 18

If $x^2 = -16$, what are the solutions?

Accepted Answer

$x = 4i$ and $x = -4i$

Question 19

Complete the square for $x^2 + 6x + 5 = 0$ and solve for $x$.

Accepted Answer

$x = -1$ and $x = -5$

College Algebra Study Guide: Equations and Inequalities

Study Guide - Practice Questions