How do you solve the inequality 3<5x-4<7?

Mar 24, 2018

$\frac{7}{5} < x < \frac{11}{5}$

Explanation:

$\text{add 4 to each of the 3 intervals}$

$3 \textcolor{red}{+ 4} < 5 x \cancel{- 4} \cancel{\textcolor{red}{+ 4}} < 7 \textcolor{red}{+ 4}$

$\Rightarrow 7 < 5 x < 11$

$\text{divide each interval by 5}$

$\Rightarrow \frac{7}{5} < x < \frac{11}{5}$

$x \in \left(\frac{7}{5} , \frac{11}{5}\right) \leftarrow \textcolor{b l u e}{\text{in interval notation}}$