Solve the following inequation, write down the solution set and represent it on the real number line:
$- 2 + 10 x \leq 13 x + 10 < 24 + 10 x$ , x $ϵ$ Z.

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Solution

$- 2 + 10 x \leq 13 x + 10 \Rightarrow - 3 x \leq 12 \Rightarrow - x \leq 4 \Rightarrow x \geq - 4$
$13 x + 10 < 24 + 10 x \Rightarrow 3 x < 14 \Rightarrow x < \frac{14}{3}$
Thus the range of x values satisfying the above inequalities is $- 4 \leq x < \frac{14}{3}$
The number line depicting the range is shown above.

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