Question 1

Which of the following is TRUE about solving inequalities compared to equations?

Accepted Answer

Inequalities can have infinitely many solutions, often described using interval notation.

Question 2

What happens to the inequality sign when you multiply or divide both sides of an inequality by a negative number?

Accepted Answer

The inequality sign reverses direction.

Question 3

Solve the compound inequality $$-6 \leq 2x \u003c 4. $$What is the solution set?

Accepted Answer

$$[-3, 2)$$

Question 4

Which of the following is the correct solution set for $$|x| \leq 6$$?

Accepted Answer

$$[-6, 6]$$

Question 5

If $$|x| \u003e 3$$, which of the following intervals represents the solution set?

Accepted Answer

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

Question 6

Solve the absolute value inequality $$|3x + 3| \u003c 6.$$

Accepted Answer

Question 7

Which of the following is the correct solution set for $$|2x + 3| \geq 6$$?

Accepted Answer

$$(-\infty, -\frac{9}{2}] \cup [\frac{3}{2}, \infty)$$

Question 8

Consider the inequality $$7 - 2x \leq -3. $$What is the solution set?

Accepted Answer

$$x \geq 5$$

Question 9

Which of the following is always TRUE for any real number $$x$$?

Accepted Answer

$$|x| \u003e -5$$

Question 10

Solve the three-sided inequality $$-6 \leq 2x + 4 \u003c 2.$$

Accepted Answer

$$[-5, -1)$$

Question 11

Suppose you are solving $$x^2 - 12x$$ \u003e 0$$. What are the critical values you should test?

Accepted Answer

$$x = 0$$ and $$x = 12$$

Question 12

When solving a rational inequality, why must you check the sign of the denominator?

Accepted Answer

Because dividing by zero is undefined and can change the solution set.

Question 13

Which of the following is the correct solution set for $$x^2 - 4$$ \u003c 0$$?

Accepted Answer

$$(-2, 2)$$

Question 14

If you solve $$5x + 10 \leq 5x - 2$$, what is the solution set?

Accepted Answer

$$\emptyset$$

Question 15

Which of the following is the correct solution set for $$|x - 2| \u003c 0$$?

Accepted Answer

$$\emptyset$$

Question 16

Given the compound inequality $$2 \u003c x \leq 5$$, which of the following is the correct interval notation?

Accepted Answer

$$(2, 5]$$

Question 17

Which of the following is the correct solution set for $$|x| \geq 0$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 18

If $$x$$ satisfies $$x^2 + 12x$$ \u003c 0$$, what is the solution set?

Accepted Answer

$$(-12, 0)$$

Question 19

Which of the following is the correct solution set for $$|x| \u003c 0$$?

Accepted Answer

$$\emptyset$$

Question 20

A medical test measures the distance of a value $$x$$ from a reference point $$a$$ and requires $$|x - a| \geq 1. $$What does this mean in terms of $$x$$?

Accepted Answer

$$x is at $$least 1 unit away from $$a.$$

Study Notes: Solving Inequalities in Precalculus

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