Solve the inequality and show the graph of the solution on number line:
$3 (1 - x) < 2 (x + 4)$

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Solution

Given, $3 (1 - x) < 2 (x + 4)$
$\Rightarrow 3 - 3 x < 2 x + 8$
$\Rightarrow 3 - 8 < 2 x + 3 x$
$\Rightarrow - 5 < 5 x$
$\Rightarrow x > - 1 or x \in (- 1, \infty)$
Blue line is $y = 3 - 3 x$ and red line is $y = 2 x + 8$
Both line intersect at $x = - 1$ and It is clearly observed from graph that
For $x > - 1 \Rightarrow 2 x + 8 > 3 - 3 x$

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