Absolute Value Equations (Special Cases)

Solve for x
l 5x l = 40

• x = 8 and x =-8
• x = 35 and x = -35
• Only x = 8
• No Solution

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 4x−3 l = 17

• x = 5 and x =-3.5
• x = 0 and x = -5
• x = 10 and x = -10
• No Solution

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

∣ 2x + 9 ∣ = 15

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

Solve |x – 12| - 3 = 11.

• x = -2
  x = -26
• x = -2
  x = 26
• x = 3
  x = 25
• x = 4
  x =  -7

Solve for x

l 5x l = -40

• x = 8 and x =-8

• x = 35 and x = -35

• Only x = 8

• No Solution

Solve for x

l x−6 l + 14= 10

• x = 12 and x = 0

• x = 3 and x = -3

• x = -12 and x = 0

• No Solution

Solve for x

l 2x−1 l +12 = 8

• x = 2.5 and x = -1.5

• x = 2 and x = -1

• x = -2 and x = 9

• No Solution