Solve the equation and write the solution set.

|4x - 8| - 3x = 6x + 2

|4x-8|-3x=6x+2

Add 3x to both sides.

|4x-8|-3x+3x=6x+2+3x

|4x-8|=9x+2

Solve Absolute Value.

|4x-8|=9x+2

4x-8=9x+2 or 4x-8 = - (9x+2)

4x-8=9x+2

4x-8-9x=9x+2-9x (Subtract 9x from both sides)

-5x-8=2

-5x-8+8=2+8 (Add 8 to both sides)

-5x=10

-5x/-5 = 10/-5 (Divide both sides by - 5)

x=-2

4x-8 = - (9x+2)

4x-8=-9x-2 (Simplify both sides of the equation)

4x-8+9x=-9x-2+9x (Add 9x to both sides)

13x-8=-2

13x-8+8=-2+8 (Add 8 to both sides)

13x=6

13x/13=6/13 (Divide both sides by 13.)

x = 6/13