Solve the inequality 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,
$5 (2 x - 7) - 3 (2 x + 3) \leq 0$
$\Rightarrow 10 x - 35 - 6 x - 9 \leq 0$
$\Rightarrow 4 x - 44 \leq 0 \Rightarrow x \leq 11$
And $2 x + 19 \leq 6 x + 47$
$\Rightarrow 2 x - 6 x \leq 47 - 19$
$\Rightarrow - 4 x \leq 28 \Rightarrow x \geq - 7$
Thus using above two we have $- 7 \leq x \leq 11$
Solution is also shown graphically

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