Solve the inequalities in Exercieses 7 to 10 and represent the solution graphically on number line:

$5 (2 x - 7) - 3 (2 x + 3) \leq 0, 2 x + 19 \leq 6 x + 47$

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Solution

We have

$5 (2 x - 7) - 3 (2 x + 3) \leq 0$

and $2 x + 19 \leq 6 x + 47$

$\Rightarrow 10 x - 35 - 6 x - 9 \leq 0$ and $- 4 x \leq 28$

$\Rightarrow 4 x - 44 \leq 0$ and $x \geq - 7$

$\Rightarrow 4 x \leq 44$ and $x \leq - 7$

$\Rightarrow x \leq 11$ and $x \leq - 7$

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