Question

Which of the following is the simplified form of $\frac{-4x}{10}\ge \frac{32}{5}$?

• A. $x\le 16$
• B. $x\le -16$
• C. $x\ge 16$
• D. $x\ge -16$

Answer 1

The correct option is B $x\le -16$

Given algebraic inequality, $\frac{-4x}{10}\ge \frac{32}{5}$

We know that on multiplying a positive number on both sides of an algebraic inequality, the inequality sign remains same.

On multiplying both the sides of the inequality by $10$, we get,
$\frac{-4x}{10}\times 10\ge \frac{32}{5}\times 10$

$\Rightarrow -4x\ge 64$

We know that on dividing a negative number on both sides of an algebraic inequality, the inequality sign gets flipped.

On dividing both the sides of the inequality($-4x\ge 64$) by $-4$, we get,

$\frac{-4x}{-4}\le \frac{64}{-4}\Rightarrow x\le -16$