# What is the solution set for #abs(x – 2) + 4 = 3#?

##### 1 Answer

Aug 26, 2015

#### Explanation:

As it is written, your absolute value equation has **no real solutions**.

That happens because the absolute value of any real number always returns the **positive** value of said number, irrespective of its sign.

In your case, you know that if you isolate the modulus on one side of the equation by adding

#|x-2| + color(red)(cancel(color(black)(4))) - color(red)(cancel(color(black)(4))) = 3-4#

#|x-2| = -1#

In this case, you need the absolute value of a real number, which is what *negative*.

This contradicts the definition of the absolute value, which implies that