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Q. Solve the inequality $ 3x+2>-16,\,2x-3\le 11 $

J & K CETJ & K CET 2014Linear Inequalities

Solution:

We have, $ 3x+2>-16 $
$ \Rightarrow $ $ 3x>-16-2 $
$ \Rightarrow $ $ x>\frac{-18}{3} $
$ \Rightarrow $ $ x>-6 $ and $ 2x-3\le 11 $
$ \Rightarrow $ $ 2x\le 11+3\Rightarrow 2x\le 14 $
$ \Rightarrow $ $ x\le \frac{14}{2}\Rightarrow x\le 7 $
$ \therefore $ Solution of given inequalities is $ x\in (-6,\,7] $