Solving Linear Absolute Value Equations and Inequalities

What must be true about the right-hand side of an absolute value equation for it to have solutions?

• It must be a fraction.

• It must be an integer.

• It must be zero or positive.

• It must be negative.

When solving the equation |a| = b, what are the two equations you need to solve?

• a = b and a = 0

• a = b and a = -b

• a = b and a = b + 1

• a = b and a = b - 1

If |x - 1| = 4, what are the solutions for x?

• x = 3 or x = -5

• x = 4 or x = -4

• x = 5 or x = -3

• x = 2 or x = -2

How do you solve the inequality |a| < b?

• a > b or a < -b

• a < b or a > -b

• a > b and a < -b

• a < b and a > -b

What is the solution set for the inequality |2x + 3| < 15?

• -9 < 2x + 3 < 9

• -15 < 2x + 3 < 15

• -18 < 2x + 3 < 12

• -12 < 2x + 3 < 18

What is the result of solving the compound inequality -18 < 2x + 3 < 12?

• -15 < x < 15

• -12 < x < 18

• -6 < x < 9

• -9 < x < 6

What should you do to solve the inequality |2x - 1/3| ≥ 5/6?

• Divide both sides by 6

• Divide both sides by 3

• Multiply both sides by 6

• Multiply both sides by 3

What is the solution for the inequality 2x - 1/3 ≥ 5/6?

• x ≤ -7/4

• x ≥ -7/4

• x ≤ 7/4

• x ≥ 7/4

What is the solution for the inequality 2x - 1/3 ≤ -5/6?

• x ≥ 3/4

• x ≤ 3/4

• x ≥ -3/4

• x ≤ -3/4

What are the possible values of x for the inequality |2x - 1/3| ≥ 5/6?

• x ≤ 7/4 or x ≥ -3/4

• x ≤ 3/4 or x ≥ -7/4

• x ≥ 3/4 or x ≤ -7/4

• x ≥ 7/4 or x ≤ -3/4