# How do you solve the inequality -5<=x+8<15?

Apr 25, 2017

See the entire solution process below:

#### Explanation:

Subtract $\textcolor{red}{8}$ from each segment of the system of inequalities to solve for $x$ while keeping the system balanced:

$- 5 - \textcolor{red}{8} \le x + 8 - \textcolor{red}{8} < 15 - \textcolor{red}{8}$

$- 13 \le x + 0 < 7$

$- 13 \le x < 7$

Or

$x \ge - 13$ and $x < 7$

Or, in interval form:

$\left(- 13 , 7\right]$

Apr 25, 2017

-13$\le$x$<$ 7

#### Explanation:

There are two ways to do this.

The first way is to separate the inequalities and go from there,

Given:
-5$\le$x + 8$<$ 15

Separated:
-5$\le$x + 8 , and x + 8$<$15

Then simply solve for x by subtracting 8:
-13$\le$x , and x$<$7

Finally combine to get:
-13$\le$x$<$ 7

The second method to solve this is to do it together,

Given:
-5$\le$x + 8$<$ 15

Subtract 8 from both sides and get the answer:
-13$\le$x$<$ 7