Question

How do you solve `4|x + 5| + -6 = 34`?

Answer 1

`x = 5, x = -15`

Explanation:

Given: `4|x+5| + -6 = 34`

Start by adding `6` to both sides of the equation:

`4|x+5| + -6 + 6 = 34 + 6`

Simplify: `4|x+5| = 40`

Divide both sides by `4`: `(4|x+5|)/4 = 40/4`

Simplify: `|x+5| = 10`

Break the function into two equations:
`y = |x+a| " is " y = x +a" and " y = -(x+a)`

`|x+5| = 10 " is " x+5 = 10 " and " -(x+5) = 10`

Solve each equation:

`x+5 = 10`
`x+5 - 5 = 10 - 5`
`x = 5`

`-(x+5) = 10`
`-x - 5 = 10`
`-x -5 + 5 = 10 + 5`
`-x = 15`
`x = -15`

Check answers :
`4|5+5| + -6 = 4*10 -6 = 40 - 6 = 34`
`4|5 + -15| + -6 = 4|-10| - 6 = 4(10) - 6 = 34`