Solving and Graphing Absolute Value Equations and Inequalities

Describe the movements.

y= −|x|+4

• Left 4, Down 1

• Reflect over x-axis, Down 4

• Reflect over x-axis, Up 4

• Right 4, Up 1

Solve for x
l 2x−1 l = 9

• x = 5 and x =-4

• x = 5 and x = -5

• Only x = 5

• No Solution

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|d - 4| ≥ 12

• d = -8 or d = 0

• no solution

• d ≥ 8 or d ≤ 0

• d = 40 or d = 32

• A
• B
• C
• D

Solve for x
2 lx−4l+8=18

• x = 9 and x =-1

• x = 1 and x = -9

• x= 4 and x = -2

• No Solution

 |−2n| + 10 = −50

• {30, -30}

• {20,-20}

• {-5,5}

• No Solution

Solve.

|x + 4| < 5

• x < -9 or x > 1

• -9 < x < 1

• x < 9 or x > -1

• -1 < x < 9

Solve.
|y - 4| ≥ 8

• y ≤ -4 or y ≥ 12

• -4 ≤ y ≤ -12

• y ≤ 4 or y ≥ -12

• -12 ≤ x ≤ 4