Solve for |2x + 4|-1=7

x = - 6 or x = 2

Step-by-step explanation:

The absolute value function always returns a positive value. However, the expression inside can be positive or negative.

Given

| 2x + 4 | - 1 = 7 (add 1 to both sides)

| 2x + 4 | = 8, thus

2x + 4 = 8 (subtract 4 from both sides)

2x = 4 (divide both sides by 2)

x = 2

OR

- (2x + 4) = 8

- 2x - 4 = 8 (add 4 to both sides)

- 2x = 12 (divide both sides by - 2)

x = - 6

As a check

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

x = 2 → | 4 + 4 | - 1 = | 8 | - 1 = 8 - 1 = 7 ← True

x = - 6 → | - 12 + 4 | - 1 = | - 8 | - 1 = 8 - 1 = 7 ← True

Hence the solutions are x = - 6 or x = 2