Solve the inequation $2 x - 8 \leq 17 - 3 x$ and find the maximum value of $x$ . Also, represent the solution set on a number line.

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Solution

Step 1: Solve the inequation
$\Rightarrow 2 x - 8 \leq 17 - 3 x \Rightarrow 2 x + 3 x \leq 17 + 8 \Rightarrow 5 x \leq 25 \Rightarrow x \leq \frac{25}{5} \Rightarrow x \leq 5$
The solution set of the inequality will be $x \in (- \infty, 5]$ and the maximum value of $x$ will be $5$ .
Step 2: Represent the solution set on the number line
Thus, the solution set of the given inequation is $x \in (- \infty, 5]$ and the maximum value of $x$ is $5$ .

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