Question

How do you solve `abs(x-4)+1=8`?

Answer 1

First, isolate the absolute value term and then solve the term inside the absolute value function for both its negative and positive equivalent.

Explanation:

Step 1) Subtract `color(red)(1)` from each side of the equation to isolate the absolute value term and keep the equation balanced:

`abs(x - 4) + 1 - color(red)(1) = 8 - color(red)(1)`

`abs(x - 4) + 0 = 7`

`abs(x - 4) = 7`

Step 2) Because the absolute value is a special case we need to find two solutions. The absolute value function takes either a positive or negative number and transforms it into its positive equivalent. Therefore we need to solve the expression within the absolute value for both the negative and positive equivalent.

Solution 1)

`x - 4 = 7`

`x - 4 + 4 = 7 + 4`

`x - 0 = 11`

`x = 11`

Solution 2)

`x - 4 = -7`

`x - 4 + 4 = -7 + 4`

`x - 0 = -3`

`x = -3`

The solutions are 11 and -3