Absolute Value Equations and Inequalities

Solve for x
∣ 2x + 9 ∣ = 15

• x = 3 
• x = 3   x = -6
• x = 3   x = -12
• x = 6   x = -12

An absolute value can NOT equal...

• a positive number
• a negative number

Solve for x 
|−2n| + 10 = −50

• {30, -30}
• {20,-20}
• {-5,5}
• No Solution

Solve for x
| m - 2 | < 8

• 9 > m > 8
• 2 < m < -6
• -6 < m < 10
• 0 > m < 0

Solve for x
| x - 7 | > 3

• x>4 or x<10
• 4 < x < 10
• x>10 and x<4
• x>10 or x<4

Solve for x
| 2x – 3 | + 5 =10.

• { -1, 1 }
• { -1, 4 }
• { -1, -4 }
• { 1, 4 }

Solve for x
l 2x−1 l +4 = 8 

• x = 2.5 and x = -1.5
• x = 2 and x = -1
• x = -2 and x = 9
• No Solution

Solve for x
∣ -2x + 9 ∣ > 15

• x<-3 or x>12
• -3 < x < 12
• x<-3 and x>12
• -3 < x > 12

Solve for x
| 6 - 2x | = -5

• 11/2, 1/2
• -5, 5
• 1, 3
• ⊘ No solution

Describe the movements. 
y = − | x | + 4

• Left 4, Down 1
• Reflect x-axis, Down 4
• Reflect x-axis, Up 4
• Right 4, Up 1