# What is the solution to the inequality #abs(x-4)>3#?

##### 1 Answer

#### Explanation:

You already have the modulus isolated on one side of the inequality, so you don't need to worry about that.

By definition, the absolute value of any real number will **always be positive**, regardless of the sign of said number.

This means that you need to take into account two scenarios, one in which

#x-4>=0 implies |x-4| = x-4#

The inequality becomes

#x - 4 > 3 implies x > 7#

#x-4<0 implies |x-4| = -(x-4)#

This time, you get

#-(x-4) > 3#

#-x + 4 > 3#

#-x > -1 implies x< 1#

This means that your solution set for this absolute value euqation will include any value of **bigger** than **smaller** than

#x in (-oo, 1) uu (7, +oo)#

For any value of