Question

Find the solution set of each of the following inequation:
$\frac{1}{2}(x-3)\ge \frac{2}{3}(6-2x),xϵR$

Answer 1

$Given:\frac{1}{2}(x-3)\ge \frac{2}{3}(6-2x)$
$\Rightarrow 6\times \frac{1}{2}(x-3)\ge 6\times \frac{2}{3}(6-2x)$
[Multiplying both sides by 6]
$\Rightarrow 3(x-3)\ge 4(6-2x)$
$\Rightarrow 3x-9\ge 24-8x$
$\Rightarrow 3x-9+9\ge 24-8x+9$
[Adding 9 to both sids]
$\Rightarrow 3x\ge 33-8x$
$\Rightarrow 3x+8x\ge 33-8x+8x$
[Adding 8x to both sides]
$\Rightarrow 11x\ge 33$
$\Rightarrow \frac{11x}{11}\ge \frac{33}{11}$
[Dividing both sides by 11]
$\Rightarrow x\ge 3$
Hence, the solution set is $\{x:x\ge 3,xϵR\}$