Solving Absolute Value Inequalities: A Comprehensive Guide

What is the first step when solving an absolute value inequality?

• Square both sides

• Multiply both sides by a constant

• Write two equations

• Combine like terms

When changing the inequality direction, what else must be done?

• Add a constant to both sides

• Change the sign of the constant inside the absolute value

• Multiply both sides by -1

• Square both sides

How do you represent the solution of an inequality on a number line?

• With a closed circle and shading

• With an open circle and shading

• With a point and a line

• With a dashed line

What is the interval notation for the solution x > 2 or x < -4/3?

• (-∞, 2) ∪ (-4/3, ∞)

• (-4/3, 2)

• (-∞, -4/3) ∩ (2, ∞)

• (-∞, -4/3) ∪ (2, ∞)

What should be done first when the absolute value expression is not isolated?

• Divide both sides by a constant

• Multiply both sides by a constant

• Subtract a constant from both sides

• Add a constant to both sides

What happens to the inequality direction when dividing by a negative number?

• It changes direction

• It becomes an equality

• It becomes undefined

• It remains the same

What are the two equations derived from |2x - 1| ≥ 5?

• 2x - 1 ≥ 5 and 2x - 1 ≤ 5

• 2x - 1 ≥ 5 and 2x - 1 ≤ -5

• 2x - 1 ≤ 5 and 2x - 1 ≥ -5

• 2x - 1 ≥ 5 and 2x - 1 = 5

What is the solution for 2x - 1 ≥ 5?

• x ≥ 3

• x ≥ 2

• x ≥ 5

• x ≥ 4

What is the solution for 2x - 1 ≤ -5?

• x ≤ -5

• x ≤ -4

• x ≤ -3

• x ≤ -2

What is the interval notation for the solution x ≤ -2 or x ≥ 3?

• (-∞, -2] ∪ [3, ∞)

• (-∞, -2) ∪ (3, ∞)

• (-∞, -2] ∩ [3, ∞)

• (-2, 3)