The solution set of the equation |5x-12|=x is what?

Answer 1

Since what's inside the absolute value sign can be positive or negative, we have two equations.

5x - 12 = x

4x = 12

x = 3

5x - 12 = -x

6x = 12

x = 2

Let's check.

|5(3) - 12| = 3

|15 - 12| = 3

|3| = 3

3 = 3

0 = 0

True

|5(2) - 12| = 2

|10 - 12| = 2

|-2| = 2

2 = 2

0 = 0

Also true