When doing inequalities if you divide by a negative you swit

When doing inequalities, if you divide by a negative, you switch the sign, does this also apply to absolute value problems?

Solution

In absolute value problems we have to consider two case,

Suppose absolute value |a-5|< 8

Case:- 1- For a>=5,

|a-5|= a-5

so, inequality a-5<8 --> a<13

Case:-2- For a<5

then, |a-5|=-(a-5)

so, inequality -(a-5)<8

                      a-5>-8

                       a>-3

So, we can write given inequality |a-5|<8--->    -8<a-5<8