Understanding Absolute Value Equations and Inequalities

What does the absolute value of a number represent?

• The negative of the number

• The distance from zero on a number line

• The square of the number

• The number itself

What are the solutions to the equation |x| = 2?

• x = 2 only

• x = 0

• x = 2 and x = -2

• x = 1 and x = -1

Which of the following represents the inequality |x| < 2?

• x < -2 or x > 2

• x = 2 or x = -2

• x > 2

• -2 < x < 2

How is the inequality |x| > 2 represented on a number line?

• A single point at -2

• A shaded region outside -2 and 2

• A shaded region between -2 and 2

• A single point at 2

What is the solution to the equation |2x - 3| = 5?

• x = 2 and x = -2

• x = 3 and x = -3

• x = 5 and x = -5

• x = 4 and x = -1

For the inequality |2x - 3| < 5, what is the range of x?

• x = 1 or x = -1

• x > 1

• x < -1 or x > 4

• -1 < x < 4

In the inequality |2x - 3| > 5, which values of x satisfy the inequality?

• x = -1

• -1 < x < 4

• x > 4 or x < -1

• x = 4

What is the first step in solving an absolute value equation?

• Add a constant to both sides

• Isolate the absolute value expression

• Multiply both sides by a constant

• Square both sides

How do you express the inequality |x| ≤ 3 algebraically?

• -3 ≤ x ≤ 3

• x = 3 or x = -3

• x < -3 or x > 3

• x > 3

What does it mean if an absolute value inequality is written as |x| ≥ 4?

• x is exactly -4

• x is between -4 and 4

• x is greater than 4 or less than -4

• x is exactly 4