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

Dec 19, 2016

$x = 3$ 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:

$\left\mid 8 x + 8 \right\mid + 3 - \textcolor{red}{3} = 35 - \textcolor{red}{3}$

$\left\mid 8 x + 8 \right\mid + 0 = 32$

$\left\mid 8 x + 8 \right\mid = 32$

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)

$8 x + 8 = 32$

$8 x + 8 - \textcolor{red}{8} = 32 - \textcolor{red}{8}$

$8 x + 0 = 24$

$8 x = 24$

$\frac{8 x}{\textcolor{red}{8}} = \frac{24}{\textcolor{red}{8}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}}} = 3$

$x = 3$

Solution 2)

$8 x + 8 = \textcolor{red}{-} 32$

$8 x + 8 - \textcolor{red}{8} = - 32 - \textcolor{red}{8}$

$8 x + 0 = - 40$

$8 x = - 40$

$\frac{8 x}{\textcolor{red}{8}} = - \frac{40}{\textcolor{red}{8}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}}} = - 5$

$x = - 5$