Question

Solve the inequality for real $x$.

$\frac{1}{2}(\frac{3x}{5}+4)\ge \frac{1}{3}(x-6)$

Answer 1

Given, $\frac{1}{2}(\frac{3x}{5}+4)\ge \frac{1}{3}(x-6)$

$\Rightarrow 3(\frac{3x}{5}+4)\ge 2(x-6)$

$\Rightarrow \frac{9x}{5}+12\ge 2x-12$

$\Rightarrow 12+12\ge 2x-\frac{9x}{5}$

$\Rightarrow 24\ge \frac{10x-9x}{5}$

$\Rightarrow 24\ge \frac{x}{5}\Rightarrow x\le 120\text{or}x\in (-\infty ,120]$