How do you solve the inequality 4.5x - 3.8 ≥ 1.5x - 2.3?

Jan 3, 2016

$x \ge 0.5 = \frac{1}{2}$

Explanation:

$4.5 x - 3.8 \ge 1.5 x - 2.3$

Subtract $1.5 x$ from both sides

$\implies 4.5 x - 3.8 - 1.5 x \ge 1.5 x - 2.3 - 1.5 x$
$\implies 3 x - 3.8 \ge - 2.3$

Add $3.8$ to both sides

$\implies 3 x - 3.8 + 3.8 \ge - 2.3 + 3.8$
$\implies 3 x \ge 1.5$

Divide both sides by $3$

$\implies \frac{3 x}{3} \ge \frac{1.5}{3}$
$\implies x \ge 0.5 = \frac{1}{2}$