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?

A. x − 4 = −7
B. x + 4 = −7
C. −x − 4 = 7
D. x + 4 = 7

Answer 1

Option A is correct

`x-4 = -7`

Explanation:

Absolute function:

The parent function f(x) = |x| is defined as:

f(x) = x if x> 0

and

f(x) = -x if x<0

Given the equations:

`|x-4|+1 = 8`

Step 1.

`|x-4|+1 = 8`

Step 2.

subtract 1 from both sides we have;

`|x-4|= 8-1`

Step 3.

Simplify:

`|x-4|=7`

By definition of absolute function:

x-4 = -7 and x -4 = 7

Therefore, the following is a correct next step to solve the equation is,
`x-4 = -7`