# Solve absolute value inequality : 5>|4-x|

Solve absolute value inequality :
5>|4-x|
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Gerald Lopez
Given,
5>|4-x|
On simplification, we get
5>|4-x|
$⇒|4-x|<5$

$⇒-5-4<4-x-4<5-4$ [Subtracting 4]
$⇒-9<-x<1$
$⇒\frac{-9}{-1}>\frac{-x}{-1}>\frac{1}{-1}$ [Dividing -1. When divided by a negative number, the sign will get reversed.]
$⇒9>x\succ 1$
$⇒-1
$⇒x\in \left(-1,9\right)$