|2x+6|-7=40

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Solve the following equation

|2x+6|-7=40

Solve for x

|2x+6|-7 = 40

We add 7 to each side

|2x + 6| - 7 + 7 = 40 + 7

|2x + 6| = 47

Absolute Value Equations

Since this is an absolute value equation
Setup two equations

• 2x+6 = 47
• 2x+6 = -47

Solve Equation 1 → 2x+6 = 47

Subtract - 6 from both sides of the equation

2x+6 - 6= 47 - 6

2x = 41

Divide each side of absolute value equation 1 by 2

Keep our =

Solution to absolute value equation 1 is

x = 20.5

Solve Equation 2 → 2x+6 = -47

Subtract - 6 from both sides of the equation

2x+6 - 6= -47 - 6

2x = - 53

Divide each side of absolute value equation 2 by 2

Keep our =

Solution to absolute value equation 2 is

x = -26.5