Question
Solve the inequality: $-12<4-\frac{3 x}{-5} \leq 2$

Answer

Given inequality is; $-12<4-\frac{3 x}{-5} \leq 2$
$\Rightarrow-12<4-\frac{3 x}{-5} \leq 2$
$\Rightarrow$ - 12 - 4 < 4 - $\frac{3 x}{-5}$ - 4 $\le$ 2 - 4 [subtracting by 4]
$\Rightarrow-16<\frac{-3 x}{-5} \leq-2$
$\Rightarrow-16<\frac{3 x}{5} \leq-2$
Multiplying the inequality by 5.
$\Rightarrow-16 \times 5<\frac{3 x}{5} \times 5 \leq-2 \times 5$
$\Rightarrow$ -80 < 3x $\le$ -10
$\Rightarrow-\frac{80}{3}<x \leq-\frac{10}{3}$
$\therefore$ all real numbers x greater than $-\frac{80}{3}$ but less than or equal to $-\frac{10}{3}$ are a solution of given equality.
x $\in$ ($-\frac{80}{3},-\frac{10}{3}$]

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