Question

Solve the following inequations: $7x+3\ge 3x-5$ and $\frac{x}{4}-5\le \frac{5}{4}-x,xϵR$. Also graph the solution set on the number line.

Answer 1

$7x+3\ge 3x-5and\frac{x}{4}-5\le \frac{5}{4}-x\Rightarrow 7x-3x\ge -5-3and\Rightarrow \frac{x-20}{4}\le \frac{5-4x}{4}\Rightarrow 4x\ge -8and\Rightarrow x-20\le 5-4x\Rightarrow x\ge -2and\Rightarrow x+4x\le 5+20\Rightarrow 5x\le 25\Rightarrow x\le 5$
So, $-2\le x\le 5$
The required number line is as follows: