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

Solve for k.

 $|k-9|=4$  

• 5, 13

• -5, -13

• 5, -5

• 13

Solve for x: -4|x + 5| + 2 = -126

• x = 26 or x = -36

• x = 27 or x = -37

• x = 123 or x = -133

• No Solution

What is the first step in solving this equation: |2x - 3| = 4

• Divide by 2

• Subtract 2

• Split into two parts with one part = 4 and one part = -4

• Add 3

• 4

• -4

• 12

• No Solution

Solve for x: 0.5|x + 14| - 3 = 7

• x = -6 or x = -22

• x = 6 or x = -34

• x = -9 or x = -19

• No Solution

Solve:
 $\left|2x-3\right|=15$  

•  $x=-6,\ 9$  

•  $x=-6$  

•  $x=9$  

•  $x=-9,\ 6$  

The first step you would perform to solve the following absolute value equation would be what?

5| x + 1| + 6 = 26

• Divide by 5

• Subtract 1

• Subtract 6

• Remove the absolute value notation bars

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

• No solution

• One Solution

• Two Solutions

• -80, -86

• 80, 83

• 83, 86

• -83, -86

• no solution