# How do you solve # abs(x+5)>12#?

##### 1 Answer

Aug 31, 2015

#### Explanation:

You're dealing with the absolute value of an expression, which means that you need totake into account the fact that the absolute value of a real number returns a **positive** value *regardless* of the sign of said number.

#color(blue)(|x| = {(x", "x >=0),(-x", "x<0) :}, " "(AA)x in RR)#

This means that you have to look at two possible scenarios, one in which the expression inside the modulus is positive and one in which it's negative.

#x+5 >0 implies |x+5| = x + 5#

The inequality takes the form

#x + 5 >12 implies x > 7#

#x+5<0 implies |x+5| = -(x+5)#

This time, you get

#-(x+5) > 12#

#-x - 5 > 12#

#-x > 17 implies x < -17#

The inequality will be true for any value of **greater** than **smaller** than