Question

How do you solve `|8x + 4| = 52`?

Answer 1

`x=6 or x=-7`

Explanation:

`|8x +4|=52`
Solve for the absolute value
We know either `8x + 4=52 or 8x +4 = -52`
We gonna call the first one possibility ONE and the second one possibility TWO.

Let's start by solving the first possibility
`8x + 4 =52`
Subtract `color(red)(4)` from both sides
`8x cancel(+4) cancelcolor(red)(-4) = 52 - color(red)(4)`
`8x = 48`
Divide both sides `8`
`(cancel8x)/cancel8 = 48/8`
`x= 6`

Then, solve the second possibility
`8x +4=-52`
Let's start by subtracting `color(red)(4)` from both sides
`8x cancel(+4) cancelcolor(red)(-4)= -52 - color(red)(4)`
`8x = -56`
Divide both sides by `8`
`(cancel8x)/cancel8 = (-56)/8`
`x= -7`

Thus,

The answer is `x=6 or x=-7`