Answer:
[tex]x=2,0[/tex]
Step-by-step explanation:
STEP 1: Move all terms not containing |3x−3| to the right side of the equation.
[tex]2|3x-3|=6[/tex]
STEP 2: Divide each term by 2 and simplify.
[tex]|3x-3|=3[/tex]
STEP 3: Remove the absolute value term. This creates a ± on the right side of the equation because |x| = ±x
[tex]3x-3=[/tex] ±3
STEP 4: Set up the positive portion of the ± solution.
[tex]3x-3=3[/tex]
STEP 5: Solve the first equation for x moving all terms not containing to the right side of the equation.
[tex]3x=6[/tex]
STEP 6: Divide each term by 3 and simplify.
[tex]x=2[/tex]
STEP 7: Set up the negative portion of the ± solution.
[tex]3x-3=-3[/tex]
STEP 8: Solve the second equation for x by moving all terms not containing to the right side of the equation.
[tex]3x=0[/tex]
STEP 9: Divide each term by 3 and simplify.
[tex]x=0[/tex]
STEP 10: The solution to the equation includes both the positive and negative portions of the solution.
[tex]x=2,0[/tex]
