# If #abs(x-2)<6#, then what are the bounds of #x#? i.e. find #a# and #b# such that #a<x<b#.

##### 2 Answers

#### Explanation:

if and only if

#-6+2 < x-2+2 < 6+2# if and only if

#-4 < x < 8# .

A graph often helps to visualise inequalities:

graph{(y-|x-2|)(y-6)=0 [-6.5, 13.5, -1.4, 8.6]}

#### Explanation:

When an absolute value inequality has an upper limit (like *magnitude* of

This means

#"-"6 < x-2 < 6# .

The final step is to isolate *adding 2 to all "sides" of the inequality*, to get

#"-"6+color(red)2 < x - 2 + color(red)2 < 6 + color(red)2 #

or

#"-"4< x < 8# .

Thus, the lower limit of