Question

Solve the following inequality:
$|5-2x|<1$

Answer 1

The given equation is

$|5-2x|<1$

therefore we have 2 cases

$i.)x>5/2,ii.)x<5/2$

in first case the inequality becomes

$2x-5<1$ implies $x<3$ and we assumed $x>5/2$

therefore the solution is $5/2<x<3$

in second case the inequality becomes

$5-2x<1$ implies $x>2$ and we assumed $x<5/2$

therefore the solution is $2<x<5/2$

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

therefore the solution is $2<x<3$