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Representation of Solutions on a Number Line

Solve the fol...

Question

Solve the following inequations: $7 x + 3 \geq 3 x - 5$ and $\frac{x}{4} - 5 \leq \frac{5}{4} - x, x ϵ R$ . Also graph the solution set on the number line.
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Solution

Solving the inequation: 1 Mark each
Answer: 1 Mark
Solution on the number line: 1 Mark

$7 x + 3 \geq 3 x - 5 a n d \frac{x}{4} - 5 \leq \frac{5}{4} - x \Rightarrow 7 x - 3 x \geq - 5 - 3 a n d \Rightarrow \frac{x - 20}{4} \leq \frac{5 - 4 x}{4} \Rightarrow 4 x \geq - 8 a n d \Rightarrow x - 20 \leq 5 - 4 x \Rightarrow x \geq - 2 a n d \Rightarrow x + 4 x \leq 5 + 20 \Rightarrow 5 x \leq 25 \Rightarrow x \leq 5$
So, $- 2 \leq x \leq 5$
The required number line is as follows:

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