Question

If $\frac{2x-14}{-3}\le -3x$, then .

• A. $x\le -2$
• B. $x\ge 2$
• C. $x\le 3$

Answer 1

The correct option is A $x\le -2$

Given, $\frac{2x-14}{-3}\le -3x$

Concept : Multiplying or dividing both sides of an inequality with a negative number changes the sign of the inequality.

$\therefore$ Multiplying with $-3$ on both sides,

$\Rightarrow \frac{2x-14}{-3}\times -3\ge -3x\times -3$

$\Rightarrow 2x-14\ge 9x$
$\Rightarrow -14\ge 7x$

$\Rightarrow \frac{-14}{7}\ge \frac{7x}{7}$

$\Rightarrow x\le -2$