Solve the following linear inequations and graph the solution set on a real number line.
$\frac{1}{3} (5 x - 8) \geq \frac{1}{2} (4 x - 7), x \in R$

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Solution

Find the solution set for $x$ .
Given,
$\frac{1}{3} (5 x - 8) \geq \frac{1}{2} (4 x - 7)$
By cross multiplication we get,
$2 (5 x - 8) \geq 3 (4 x - 7)$
$10 x - 16 \geq 12 x - 21$
By taking the like terms to one side of equation,we get,
$12 x - 10 x \leq 21 - 16$
$2 x \leq 5$
$x \leq \frac{5}{2}$
$x \leq 2 \frac{1}{2}$
As per the condition given in the equation, $x \in R$
Therefore, solution set $x : x \leq 2 \frac{1}{2}$
Set can be represented in number line as.

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