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

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Answer 1 · 2017-04-19T06:02:47

$x = 5, x = -15$

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 :
$4|5+5| + -6 = 4*10 -6 = 40 - 6 = 34$
$4|5 + -15| + -6 = 4|-10| - 6 = 4(10) - 6 = 34$

How do you solve 4|x + 5| + -6 = 344|x + 5| + -6 = 34?