# How do you solve the inequality: -1/6<= 4x-4<1/3?

Aug 31, 2015

$x \in \left[\frac{23}{24} , \frac{26}{24}\right)$

#### Explanation:

You need to isolate $x$ between the two inequality signs. Start by adding $4$ to all sides

$- \frac{1}{6} + 4 \le 4 x - \textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} < \frac{1}{3} + 4$

$\frac{23}{6} \le 4 x < \frac{13}{3}$

Now divide all sides by $4$

$\frac{23}{6} \cdot \frac{1}{4} \le \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}} < \frac{13}{3} \cdot \frac{1}{4}$

This will get you

$\frac{23}{24} \le x < \frac{13}{12}$

which is equivalent to

$\frac{23}{24} \le x < \frac{26}{24}$

In interval notation, the solution set for this compound inequality is $x \in \left[\frac{23}{24} , \frac{26}{24}\right)$.