Absolute Value Equations and Inequalities

Solve:  |x + 3| < 8

• x > 5 or x < -11

• -11 < x < 5

• x > 11 or x < -5

• 5 < x < 11

Solve:
 |x + 3| > 8

• x > 5 or x < -11

• -11 < x < 5

• x > 11 or x < -5

• -5 < x < 11

Solve for x
l x−6 l + 4= 10

• x = 12 and x = 0

• x = 3 and x = -3

• x = -12 and x = 0

• No Solution

Solve.

3|2d + 9| + 13 > 10

• d > 5 or d < -1

• d < -4 or d > 5

• No Solution

• All real numbers

• A

• B

• C

• D

• v>5 or v<-5
• v≥5 or v≤-5
• v>-5 or v<5
• all real numbers

• A

• B

• C

• D

• n > 1 or n < -7
• n > -1 or n < -7
• -7 < n < -1
• no solution

Describe the first step in solving the absolute value inequality

• Add 5 on both sides

• Divide both sides by -5

• Set up two inequalities

• no solution

• {4, -4}
• {9, -9}
• {5, -9}
• {13, -1}