Question

Match the following inequalities with their simplest forms.

• A. $x\le -5$
• B. $x\ge -9$
• C. $x\ge -7$
• D. $x>-2$

Answer 1

A. $2x+5\le -5$
$\Rightarrow 2x+5-5\le -5-5$
$\Rightarrow 2x\le -10$
Dividing by $2$,
$\Rightarrow \frac{2x}{2}\le \frac{-10}{2}\Rightarrow x\le -5$

B. $-5x-10\le 35$
$\Rightarrow -5(x+2)\le 35$
Dividing both the sides by $-5$,

$\Rightarrow \frac{-5(x+2)}{-5}\ge \frac{35}{-5}$

$\Rightarrow x+2\ge -7\Rightarrow x\ge -9$

C. $10-7x\le 59$
$\Rightarrow 10-7x-10\le 59-10$
$\Rightarrow -7x\le 49$
Dividing both the sides by $-7$,

$\Rightarrow \frac{-7x}{-7}\ge \frac{49}{-7}$

$\Rightarrow x\ge -7$

D. $8-x<10$
$\Rightarrow 8-x-8<10-8$
$\Rightarrow -x<2$
Multiplying by $-1$,
$\Rightarrow x>-2$