Question

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

Answer 1

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