# How do you solve the inequality #abs(x+14)+3 > 17#?

##### 1 Answer

#### Explanation:

Start by isolating the modulus on one side of the inequality. You can do that by adding

#|x+14| + color(red)(cancel(color(black)(3))) - color(red)(cancel(color(black)(3))) > 17 - 3#

#|x+14| > 14#

Now, you know that the absolute value of a number will **always** return a *positive value*, regardless of the sign of said number.

This means that you need to take into account two possibilities, one that the expression inside the modulus is *negative*, and the other that the expression inside the modulus is *positive*.

#x+14>0 implies |x+14| = x+14#

The inequality becomes

#x + 14 > 14 implies x > 0#

#x+14 < 0 implies |x+14| = -(x+14)#

This time, you have

#-(x+14) >14#

#-x - 14 > 14#

#-x > 28 implies x < -28#

So, in order for the original inequality to be true, you need **bigger** than **smaller** than