Question

Below are the steps to solve an equation:

Step 1: |x − 4| + 1 = 8
Step 2: |x − 4| = 8 − 1
Step 3: |x − 4| = 7
Which of the following is a correct next step to solve the equation?
x − 4 = −7
x + 4 = −7
−x − 4 = 7
x + 4 = 7

Answer 1

The only answer is choice A) x-4 = -7

The rule is that if |x| = k, for some positive number k, then x = k or x = -k

Based on this rule, the absolute value equation
|x-4| = 7
breaks down into these two equations
x-4 = 7 or x-4 = -7