Question

$\frac{3+12x}{4}\ge \frac{2(4x+1)}{5}$ Which of the following best describes the solution to the inequality shown above?

• A. $x\le -\frac{13}{7}$
• B. $x\ge -\frac{13}{7}$
• C. $x\le -\frac{1}{4}$
• D. $x\ge -\frac{1}{4}$

Answer 1

The correct option is D

$x\ge -\frac{1}{4}$

$\frac{3+12x}{4}\ge \frac{2(4x+1)}{5}$
$(3+12x)\times 5\ge 2(4x+1)\times 4$
$15+60x\ge 32x+8$
$60x-32x\ge 8-15$
$28x\ge -7$
$x\ge -\frac{7}{28}$
$x\ge -\frac{1}{4}$