What is the solution set for the equation |3x-1| = x+5

Find the solution set for the equation below:
|3x-1| = x+5?

|3x-1| = x+5
Case 1:
3x-1 = x+5
3x-x = 5+1
2x = 6
x = 3

Case 2:
-(3x-1) = x+5
-3x + 1 = x+5
-3x-x = 5-1
-4x = 4
x = -1

The equation is satified for x = -1 and x = 3

The answer is x = -1, x = 3

The steps:

|3x -1| = x + 5 => a modulus means that the equation is always positive, therefore x contains 2 possible value (positive and negative)

assuming x is a -ve value,
-(3x-1) = x + 5
-3x +1 = x +5
-3x - x = 5 -1
-4x = 4
x = -1

assuming that x is a +ve value,
3x - 1 = x + 5
3x - x = 5 + 1
2x = 6
x = 3

3x-1=x+5
subtract x from both sides and add 1 to both sides
2x=6
divide both sides by 2
x=3

-3x+1=x+5 (*it's now -3x+1 instead of 3x-1 because you change both the signs in the equation that's in the absolute value)
subtract x and 1 from both sides
-4x=4
x=-1

so your answers are 3 and -1