Solve the following inequation and represent the solution set on the number line ?
$- 3 < - \frac{1}{2} - \frac{2 x}{3} \leq \frac{5}{6}, x ϵ R$

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Solution

$G i v e n : - 3 < - \frac{1}{2} - \frac{2 x}{3} \leq \frac{5}{6}, x ϵ R . \Rightarrow - 18 < 3 - 4 x \leq \frac{5}{6} \Rightarrow - 15 < - 4 x; - 4 x \leq 8 \Rightarrow x < \frac{15}{4}; x \geq - 2 \Rightarrow x < 3.75; x \geq - 2 S o l u t i o n s e t = {- 2 \leq x < 3.75, x ϵ R}$

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