Q: If $f(x) = \frac{9}{x^2}$, what is the domain of $f(x)$?

$(-\infty, 0) \cup (0, \infty)$

Q: Which of the following is true about the solution set of an inequality?

It contains all values that make the inequality true.

Question 1

Which of the following is the correct definition of an inequality?

Accepted Answer

A sentence with $<$, $>$, $\leq$, or $\geq$ as its verb.

Question 2

Solve the inequality $3x - 5 \leq 6 - 2x$ and write the solution in interval notation.

Accepted Answer

$(-\infty, 2]$

Question 3

Which principle states that if you add or subtract the same number from both sides of an inequality, the inequality remains true?

Accepted Answer

The Addition Principle for Inequalities

Question 4

What must you do when you multiply or divide both sides of an inequality by a negative number?

Accepted Answer

Reverse the inequality sign.

Question 5

Solve the compound inequality $-3 < 2x + 5 \leq 7$ and write the solution in interval notation.

Accepted Answer

$(-4, 1]$

Question 6

Which of the following is a compound inequality that represents a conjunction?

Accepted Answer

$x > 2$ and $x < 5$

Question 7

Solve the disjunction $2x - 5 \leq -7$ or $2x - 5 > 1$ and write the solution in interval notation.

Accepted Answer

$(-\infty, -1] \cup (3, \infty)$

Question 8

Find the domain of the function $f(x) = \sqrt{5 - 2x} + 1$.

Accepted Answer

$(-\infty, 2.5]$

Question 9

Natalia can be paid either $\$120$ plus $\$10$ per hour or $\$20$ per hour for a job that takes $n$ hours. For what values of $n$ is Plan B better for Natalia?

Accepted Answer

$n > 12$

Question 10

Curt can be paid $\$1500$ per month plus a commission of $10\%$ of sales, or $\$1150$ per month plus a commission of $15\%$ of sales. For what amount of monthly sales $s$ is Plan B better than Plan A?

Accepted Answer

$s > 7000$

Question 11

Which of the following best describes the solution set of $x > 2$ and $x < 5$?

Accepted Answer

$2 < x < 5$

Question 12

If $f(x) = \frac{9}{x^2}$, what is the domain of $f(x)$?

Accepted Answer

$(-\infty, 0) \cup (0, \infty)$

Question 13

Which of the following is true about the solution set of an inequality?

Accepted Answer

It contains all values that make the inequality true.

Question 14

If $x$ is a real number and $a < b$, which of the following is always true?

Accepted Answer

$a + x < b + x$

Question 15

Which of the following is a correct application of the multiplication principle for inequalities?

Accepted Answer

If $a < b$ and $c > 0$, then $ac < bc$

Solving and Understanding Inequalities in College Algebra

Study Guide - Practice Questions

Study Guide - Flashcards