absolute value equation

Question

|x + 4| + 6 = 1

Answer 1

Silvana, there is no value for x that will work in this problem. Why? Because absolute value is the distance from 0 and distance is always measured positively, absolute value is always positive.

 

There is no positive number to which you can add 6 and get 1.

Answer 2

There is no solution to this equation. 

 

First you subtract 6 from both sides to wind up w 

 

|x+4|=-5

 

since all absolute values must be >=0

there are no solutions or the null set is the answer to this.