Solve the following inequation, write the solution set and represent it on the number line.
$- 3 (x - 7) \geq 15 - 7 x > \frac{x + 1}{3}, x ϵ R$

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Solution

$G i v e n - 3 (x - 7) \geq 15 - 7 x > \frac{x + 1}{3}, x ϵ R \Rightarrow - 3 x + 7 x \geq 15 - 21 \Rightarrow 4 x \geq - 6 \Rightarrow x \geq - \frac{3}{2} 15 - 7 x > \frac{x + 1}{3} \Rightarrow 45 - 21 x > x + 1 \Rightarrow - 21 x - x > 1 - 45 \Rightarrow - 22 x > - 44 \Rightarrow x < 2$
$∴ S o l u t i o n s e t = {x : x ϵ R, - \frac{3}{2} \leq x < 2}$

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