Solve for x, the inequalities Exercises. -5 2-3x 4 9 - Vidyadip

Question

Solve for x, the inequalities Exercises.
$-5\leq\frac{2-3\text{x}}{4}\leq9$

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Answer

Given that $-5\leq\frac{2-3\text{x}}{4}\leq9$
$\Rightarrow-20\leq2-3\text{x}\leq36$
$\Rightarrow-20-2\leq-3\text{x}\leq36-2$
$\Rightarrow-22\leq-3\text{x}\leq34$
$\Rightarrow\frac{22}{3}\geq\text{x}\geq\frac{-34}{3}$
Hence $\text{x}\in\Big[\frac{-34}{3}, \frac{22}{3}\Big]$

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