Question

Solve the inequality $-15<\frac{3(x-2)}{5}\le 0$

Answer 1

Given $-15<\frac{3(x-2)}{5}\le 0$
Multiplying by $5$ on all sides
$\Rightarrow -15\times 5<\frac{3(x-2)}{5}\times 5\le 0\times 5$
$\Rightarrow -75<3(x-2)\le 0$
$\Rightarrow -75<3x-6\le 0$
Adding $6$ on all sides
$\Rightarrow -75+6<3x-6+6\le 0+6$
$\Rightarrow -69<3x\le 6$
Divide by $3$ on all sides
$\Rightarrow \frac{-69}{3}<\frac{3x}{3}\le \frac{6}{3}$
$\Rightarrow -23<x\le 2$
Hence $x\in (-23,2]$