Question

Solve the following inequality:
$|3x-2.5|⩾2$

Answer 1

The given equation is :

$|3x-2.5|\ge 2$

therefore we have 2 cases

$i.)x\ge \frac{2.5}{3}$

$ii.)x\le \frac{2.5}{3}$

in first case the inequality becomes

$3x\ge 4.5$ implies $x\ge 1.5$ and we assumed $x\ge \frac{2.5}{3}$

therefore the solution is $x\ge 1.5$

in second case the inequality becomes

$3x\le 0.5$ implies $x\le \frac{0.5}{3}$ and we assumed $x\le \frac{2.5}{3}$

therefore the solution is $x\le \frac{0.5}{3}$

now the solution of the equation is the union of the two solutions

therefore the solution is $x\in (-\infty ,\frac{0.5}{3}]\cup [1.5,\infty )$