Question

Solve the following inequalities: $\frac{1}{2}(\frac{3}{5}x+4)\ge \frac{1}{3}(x-6)$.

Answer 1

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

Multiply both sides by 6 we get

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

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

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

Multiply both sides by 5 we get

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

$\Rightarrow 9x+60\ge 10x-60$

Add -10x and -60 both sides we get

$9x+60-10x-60\ge 10x-60-10x+60$

$\Rightarrow 9x-10x\ge -60-60$

$\Rightarrow -x\ge -120$

Mltiply by $-1$ both sides we get

$\Rightarrow x\le 120$