# How do you solve -4<=-3x - 7<5?

Apr 4, 2018

$- 4 < x \le - 1$

#### Explanation:

If the expressions were more complex, we would have split the statement into two inequalities and solved them separately.

We will work with all three expressions at the same time.

Add 7 to each expression

$- 4 \textcolor{b l u e}{+ 7} \le - 3 x - 7 \textcolor{b l u e}{+ 7} < 5 \textcolor{b l u e}{+ 7}$

$3 \le \textcolor{red}{- 3} x < 12$

We will divide each term by $- 3$, but this causes the inequality signs to change.

$\frac{3}{\textcolor{red}{- 3}} \ge \frac{\textcolor{red}{- 3} x}{\textcolor{red}{- 3}} > \frac{12}{\textcolor{red}{- 3}}$

$- 1 \text{ ">=x" } > - 4$

Or

$- 4 < x \le - 1$