Exploring Absolute Value Equations and Inequalities

What is the solution to the compound inequality: 1 ≤ x < 3?

• x ≤ -2

• x > 3

• x = 5

• 1 ≤ x < 3

When solving an absolute value equation, what must be done first?

• Multiply by 2

• Add 5 to both sides

• Isolate the absolute value part

• Subtract 3 from both sides

If |x + 3| = 5, what are the possible values of x?

• x = 5 or x = -5

• x = 2 or x = -8

• x = 8 or x = -2

• x = 0 or x = -3

How do you graph the solutions of |x| = 4?

• Graph a line

• Graph two separate points at x = 4 and x = -4

• Graph a single point at x = 0

• Graph a parabola

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CCSS.HSA.CED.A.2

In the parade example, what are the two times when the float is 200 feet away from the cousin?

• t = 4 and t = 6

• t = 1 and t = 6

• t = 2 and t = 4

• t = 3 and t = 5

What should you do if an absolute value equation equals a negative number?

• Solve for x

• State that there is no solution

• Multiply both sides by -1

• Graph the solution

What are the two possible solutions for the equation |x| = 8?

• x = 8 or x = -8

• x = 4 or x = -4

• x = 2 or x = -2

• x = 0 or x = -8

How do you solve the inequality |x| ≥ 20?

• x = 20 or x = -20

• x ≤ 20 or x ≥ -20

• x > 20 or x < -20

• x < 20 or x > -20

In the athlete example, what is the allowable time range if the normal time is 224 seconds and the deviation is within 6 seconds?

• 218 to 224 seconds

• 218 to 230 seconds

• 220 to 228 seconds

• 224 to 230 seconds

What must be done to the inequality symbol when solving an absolute value inequality involving a negative value?

• Keep it the same

• Multiply by 2

• Flip the inequality symbol

• Add 5 to both sides