Question

Solve the following equation $2(2x+3)-10\le (x-2).$

Answer 1

We have
$\Rightarrow 2(2x+3)-10\le 6(x-2)$
$\Rightarrow 4x+6-10\le 6x-12$
$\Rightarrow 4x-4\le 6x-12$
$\Rightarrow 4x-6x\le -12+4$
[Transposing - 4 to RHS and 6x to LHS)
$\Rightarrow -2x\le -8\Rightarrow \frac{-2x}{-2}\ge \frac{-8}{-2}\Rightarrow x\ge 4\Rightarrow x\in [4,\infty )$
Hence the solution set of the given inequation is $[4,\infty )$ which can be graphed on real line as shown in Figure