# How do you solve #abs(x-2)<4#?

##### 1 Answer

Aug 28, 2015

#### Explanation:

You know that the absolute value of a real number is **always positive**, regardless of the sign of said number.

This means that you have two possibilities to take into account, more specifically if the expression inside the modulus is *positive* or if it is *negative*.

#x-2>=0 implies |x-2| = x-2#

The inequality will take the form

#x-2 < 4#

#x < 6#

#x-2 <0 implies |x-2| = -(x-2)#

This time, the inequality will be

#-(x-2) <4#

#-x + 2 <4#

#-x < 2 implies x > -2#

So, you've determined that any value of **bigger** than **smaller** than

The solution set will thus be