Question

How do you solve `|8x + 8| + 3 = 35`?

Answer 1

`x = 3` and `x = -5`

Explanation:

First, isolate the absolute value term on one side of the equation by doing the necessary mathematics and keeping the equation balanced:

`abs(8x + 8) + 3 - color(red)(3) = 35 - color(red)(3)`

`abs(8x + 8) + 0 = 32`

`abs(8x + 8) = 32`

Because this problem contains an absolute value term, and the absolute value function transforms a negative or positive number to the positive equivalent we must solve the term in the absolute value for both the positive and negative term the absolute value is equal to:

Solution 1)

`8x + 8 = 32`

`8x + 8 - color(red)(8) = 32 - color(red)(8)`

`8x + 0 = 24`

`8x = 24`

`(8x)/color(red)(8) = 24/color(red)(8)`

`(color(red)(cancel(color(black)(8)))x)/color(red)(cancel(color(black)(8))) = 3`

`x = 3`

Solution 2)

`8x + 8 = color(red)(-)32`

`8x + 8 - color(red)(8) = -32 - color(red)(8)`

`8x + 0 = -40`

`8x = -40`

`(8x)/color(red)(8) = -40/color(red)(8)`

`(color(red)(cancel(color(black)(8)))x)/color(red)(cancel(color(black)(8))) = -5`

`x = -5`