Solving multi-step problems involving absolute value linear equations in one variable

Match each equation with the number of solutions that it has.

• Two Solutions

• One Solution

• No solution

Solve:

 $\left|x-2\right|=3$  

• x = 5 or x = -5

• x = 5 or x = -1

• x = 5 or x = 1

• x = -5 or x = -1

What is the solution to the equation |5 - x| = 3?

• x = 2 or x = 8

• x = 2 or x = -2

• x = 5 or x = -2

• x = 5 or x = 8

Solve for x:


 $\left|x-12\right|-3=11$ 

•  $\left\{-2,-26\right\}$  

•  $\left\{-2,26\right\}$ 

•  $\left\{3,25\right\}$ 

•  $\left\{4,-7\right\}$ 

∣ 2x + 9 ∣ = 15

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Example: Solve |3x - 4| = 14

Split into 3x - 4 = 14 and 3x - 4 = -14

Solve both equations

Solutions: x = 6 and x = -3 1/3

• x = 3

• x = 3

  x = -6

• x = 3

  x = -12

• x = 6

  x = -12

Find the solution to the absolute value equation: |2 - 5x| = 10

• x = -3/5, 5/5

• x = -2/5, 4/5

• x = -8/5, 12/5

• x = -1/5, 3/5

• -70, -80

• -55, -60

• -50, 20

• 45, 25

Solve the equation: 
|2x - 5|=3

• x=1,x=4
• x=2,x=4
• x=2, x=5
• x=1

• x = 2 or x =-6
• x = -2 or x =6
• x = 2 or x =-2
• No Solutions