How do you solve #|2x-3|<2#?

2 Answers
Mar 10, 2018

Answer:

The solution is #x in (1/2,5/2)#

Explanation:

The inequality is

#|2x-3|<2#

Therefore,

#2x-3<2# and #2x-3>-2#

The first equation gives

#2x<2+3#

#x<5/2#

The second equation gives

#2x>-2+3#

#x>1/2#

Combining the #2# solutions

#x in (1/2,5/2)#

Mar 10, 2018

Answer:

#1/2 < x <5/2#

Explanation:

#"Inequalities of the type "|x|< a#

#"Always have solutions of the form"#

#-a < x < a#

#rArr-2< 2x-3 < 2#

#"add 3 to all three intervals"#

#-2color(red)(+3)< 2xcancel(-3)cancel(color(red)(+3))<2color(red)(+3)#

#rArr1< 2x <5#

#"divide all three intervals by 2"#

#rArr1/2 < x < 5/2#