Question

Solve the inequalities
$-3\le 4-\frac{7x}{2}\le 18$

Answer 1

We have,
$-3\le 4-\frac{7x}{2}\le 18$
Add $-4$ on each of the sides, we get
$-3-4\le -4+4-\frac{7x}{2}\le 18-4$
$\Rightarrow -7\le -\frac{7x}{2}\le 14$
Multiply $\frac{2}{7}$ on each of the sides
$\Rightarrow -2\le -x\le 4$
Now multiply each side by $-1$
$\Rightarrow 2\ge x\ge -4$, since after multiplying any inequalty by negative number its sign reverses
$\Rightarrow -4\le x\le 2$

$\Rightarrow x\in [-4,2]$