Solve Absolute value inequation.

Algebra 2 Tutorial

Solve Absolute value inequation.

Intro

The absolute value has two parts so like |x| can be written as x for x>=0 and -x for x<0. So we rewrite any given absolute value terms and use the property to write in two parts. We conclude the final answer by combining the final solutions using a number line or finding common sets.

Sample Problem

Solve the inequality |x-5|<4.

1<x<9


-1<x<9


1<x<-9


-1<x<-9


x<1 or x>9


Solution

It can be written in two parts.

x-5<4 and x-5>-4

Add 5 on both sides to get

x < 4+5 and x > -4+5

We get,

x<9 and x>1.

The combined solution is 1<x<9.



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