Exploring Absolute Value Equations and Inequalities

What is the absolute value of -22?

• 0

• -22

• 22

• -20

Which of the following is true about absolute values?

• Absolute values can be negative.

• Absolute values are always positive.

• Absolute values represent the distance from zero.

• Absolute values are always zero.

How many equations do you need to set up to solve an absolute value equation?

• Four

• Three

• Two

• One

What is the solution to the equation |2x - 1| = 5?

• x = 4 and x = -4

• x = 1 and x = -1

• x = 2 and x = -3

• x = 3 and x = -2

When can you split an absolute value equation into two separate equations?

• When the absolute value is added to a constant.

• When the absolute value is subtracted from a constant.

• When the absolute value is by itself on one side of the equation.

• When the absolute value is multiplied by a constant.

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

• Add the terms to both sides.

• Subtract the terms from both sides.

• Multiply the terms on both sides.

• Divide the terms on both sides.

What does the inequality |x| < 3 represent on a number line?

• x is greater than 3 or less than -3.

• x is between -3 and 3, exclusive.

• x is equal to 3 or -3.

• x is between -3 and 3, inclusive.

How do you represent the solution to |x| ≤ 3 in interval notation?

• (-3, 3)

• [-3, 3]

• (-3, 3]

• [3, -3]

What does the inequality |x| > 3 represent on a number line?

• x is between -3 and 3, inclusive.

• x is equal to 3 or -3.

• x is between -3 and 3, exclusive.

• x is greater than 3 or less than -3.

How do you represent the solution to |x| ≥ 3 in interval notation?

• [-3, 3]

• (-∞, -3] ∪ [3, ∞)

• (-3, 3)

• (-∞, -3) ∪ (3, ∞)