Solving Absolute Value Inequalities

What type of compound inequality is formed when the absolute value inequality starts with a 'less than' symbol?

• Neither

• Both

• And

• Or

How do you write the absolute value inequality |x| < 4 as a compound inequality?

• x > 4 or x < -4

• x < 4 and x > -4

• x > 4 and x < -4

• x < 4 or x > -4

What does it mean when the absolute value inequality is less than or equal to a number?

• It forms an 'or' compound inequality

• It forms an 'and' compound inequality

• It has no solution

• It forms a 'neither' compound inequality

What is the solution to the absolute value inequality |x + 1| < -5?

• x < -6 and x > 4

• No solution

• All real numbers

• x > -6 and x < 4

How do you solve the absolute value inequality |x - 2| ≤ 3?

• x - 2 ≤ 3 or x - 2 ≥ -3

• x - 2 ≥ 3 and x - 2 ≤ -3

• x - 2 ≥ 3 or x - 2 ≤ -3

• x - 2 ≤ 3 and x - 2 ≥ -3

What type of compound inequality is formed when the absolute value inequality starts with a 'greater than' symbol?

• Or

• Neither

• Both

• And

How do you write the absolute value inequality |x| > 4 as a compound inequality?

• x > 4 or x < -4

• x < 4 and x > -4

• x > 4 and x < -4

• x < 4 or x > -4

What is the solution to the absolute value inequality |4x - 2| > -8?

• x < -1.5 or x > 2.5

• No solution

• All real numbers

• x > -1.5 and x < 2.5

How do you solve the absolute value inequality |2x + 3| ≥ 1?

• 2x + 3 ≥ 1 and 2x + 3 ≤ -1

• 2x + 3 ≤ 1 or 2x + 3 ≥ -1

• 2x + 3 ≤ 1 and 2x + 3 ≥ -1

• 2x + 3 ≥ 1 or 2x + 3 ≤ -1

What is the solution to the absolute value inequality |x - 7| ≥ -5?

• No solution

• All real numbers

• x < -5 or x > 7

• x > -5 and x < 7