Question

Solve the equation. If you have one answer, type it in both boxes. If you have two answers, type your smallest answer in the first box and your largest answer in the last box. |2x – 3| = 17

x =

Answer 1

x = - 7 or x = 10

Explanation:

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

Given

| 2x - 3 | = 17, then

2x - 3 = 17 ( add 3 to both sides )

2x = 20 ( divide both sides by 2 )

x = 10

OR

- (2x - 3) = 17 ← distribute left side by - 1

- 2x + 3 = 17 ( subtract 3 from both sides )

- 2x = 14 ( divide both sides by - 2 )

x = - 7

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 = - 7 → | - 14 - 3 | = | - 17 | = 17 ← True

x = 10 → | 20 - 3 | = | 17 | = 17 ← True

Hence solutions are x = - 7 or x = 10