Solve the following inequation, write down the real number on number line:
$- 2 + 10 x \leq 13 x + 10 < 24 + 10 x, x \in Z$

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Solution

Solving left side inequation,
$- 2 + 10 x \leq 13 x + 10$
$\Rightarrow - 12 \leq 3 x$
$\Rightarrow x \geq - 4$ ......... $(1)$
Similarly , solve right side in-equation,
$13 x + 10 < 24 + 10 x$
$\Rightarrow 3 x < 14$
$\Rightarrow x < \frac{14}{3}$ ....... $(2)$
From eq. $(1)$ & $(2),$
$x \in [- 4, \frac{14}{3})$
As, $x \in Z$
Therefore, $x \in {- 4, - 3, - 2, - 1, 0, 1, 2, 3, 4}$

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