# How do you solve 2<=4-3x<7?

Feb 20, 2017

See the entire solution process below:

#### Explanation:

First, subtract $\textcolor{red}{4}$ from each segment of the inequality to isolate the $x$ term while keeping the system of inequalities balanced:

$2 - \textcolor{red}{4} \le 4 - 3 x - \textcolor{red}{4} < 7 - \textcolor{red}{4}$

$- 2 \le 4 - \textcolor{red}{4} - 3 x < 3$

$- 2 \le 0 - 3 x < 3$

$- 2 \le - 3 x < 3$

Now, divide each segment of the inequality system by $\textcolor{b l u e}{- 3}$ to solve for $x$ while keeping the system of inequalities balanced. However, remember, when dividing or multiplying an inequality by a negative number you must reverse the inequality terms:

$\frac{- 2}{\textcolor{b l u e}{- 3}} \textcolor{red}{\ge} \frac{- 3 x}{\textcolor{b l u e}{- 3}} \textcolor{red}{>} \frac{3}{\textcolor{b l u e}{- 3}}$

$\frac{2}{3} \textcolor{red}{\ge} \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{- 3}}} x}{\cancel{\textcolor{b l u e}{- 3}}} \textcolor{red}{>} - 1$

$\frac{2}{3} \textcolor{red}{\ge} x \textcolor{red}{>} - 1$