Solve the following inequation and represent the solution set on the number line:
$- 3 + x \leq \frac{8 x}{3} + 2 \leq \frac{14}{3} + 2 x$ , where $x ϵ I$
[4 MARKS]

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Solution

Steps: 2 Marks
Answer: 1 Mark
Representation of solution on number line: 1 Mark

$- 3 + x \leq \frac{8 x}{3} + 2 \leq \frac{14}{3} + 2 x, x ϵ I \Rightarrow - 3 + x \leq \frac{8 x}{3} + 2 a n d \frac{8 x}{3} + 2 \leq \frac{14}{3} + 2 x \Rightarrow - 3 - 2 \leq \frac{8 x}{3} - x a n d \Rightarrow \frac{8 x}{3} - 2 x \leq \frac{14}{3} - 2 \Rightarrow - 5 \leq \frac{5 x}{3} a n d \Rightarrow \frac{2 x}{3} \leq \frac{8}{3} \Rightarrow - 1 \leq \frac{x}{3} a n d \Rightarrow 2 x \leq 8 \Rightarrow - 3 \leq x a n d \Rightarrow x \leq 4 H e n c e, - 3 \leq x \leq 4, x ϵ I$

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