# How do you solve 7|x+2|=49?

Jan 4, 2017

Isolate the absolute value term and then solve for + and - of what it is equal to. See Explanation for full detailed process.

#### Explanation:

First step is to isolate the absolute value term by dividing each side of the equation by $\textcolor{red}{7}$ which will also keep the equation balanced.

$\frac{7 \left\mid x + 2 \right\mid}{\textcolor{red}{7}} = \frac{49}{\textcolor{red}{7}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} \left\mid x + 2 \right\mid}{\cancel{\textcolor{red}{7}}} = 7$

$\left\mid x + 2 \right\mid = 7$

Because the absolute value function transforms a negative or positive term into a positive term we must solve for the term in the absolute value function for both its positive and negative equivalent.

Solution 1)

$x + 2 = 7$

$x + 2 - \textcolor{red}{2} = 7 - \textcolor{red}{2}$

$x + 0 = 5$

$x = 5$

Solution 2)

$x + 2 = - 7$

$x + 2 - \textcolor{red}{2} = - 7 - \textcolor{red}{2}$

$x + 0 = - 9$

$x = - 9$