# How do you solve -8\leq 8x - 3< 2?

Feb 20, 2017

See the entire solution process below:

#### Explanation:

Step 1) Add $\textcolor{red}{3}$ to each segment of the system of inequalities to isolate the $x$ term while keeping the system in balance:

$- 8 + \textcolor{red}{3} \le 8 x - 3 + \textcolor{red}{3} < 2 + \textcolor{red}{3}$

$- 5 \le 8 x - 0 < 5$

$- 5 \le 8 x < 5$

Step 2) Divide each segment of the system of inequalities by $\textcolor{red}{8}$ to solve for $x$ while keeping the system in balance:

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

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

$- \frac{5}{8} \le x < \frac{5}{8}$