Question 895610: How do you solve 2/3x-6=12? I have tried turning all of it into fractions. but I am not sure on how to do that. Please help me.
Charlotte Found 3 solutions by rfer, DrBeeee, MathTherapy:Answer by rfer(16322) (Show Source): You can put this solution on YOUR website! 2/3x-6=12
2/3x=12+6
2/3x=18
x=18/(2/3)
x=18*3/2
x=54/2
x=27 Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website! You said the magic word, please.
Your problem falls into the category of "Simlify an algebraic equation."
I had the same trouble with this type of problem (many years ago) until I discovered the secret -
"Whatever arithmetic operation you do to the left side (LS) of the equation MUST be performed to the right side (RS)."
The reason is the EQUAL SIGN. If you don't do the same to each side it will not be equal anymore.
The given equation is
(1) (2/3)*x - 6 = 12
The object of simplification is to end up with only the variable (x in this case) on one side, all by itself.
Usually the first arithmetic operatio is to add or subtract terms from each side.
For the equation (1), we want to add 6 to BOTH sides to get
(2) (2/3)*x - 6 + 6 = 12 + 6 or
(3) (2/3)*x + 0 = 18 or
(4) (2/3)*x = 18
The next step is to multiply or divide BOTH sides by the same number.
For (4) multiply BOTH sides by 3 and get
(5) 3*(2/3)*x = 3*18 or
(6) 2*x = 54
Now divide BOTH sides by 2 and get
(7) 2*x/2 = 54/2 or
(8) x = 27
Thanks for reading.
Sorry, didn't have time to finish. Always check your answer.
Is (2/3*27 - 6 = 12)?
Is (2*9 - 6 = 12)?
Is (18 - 6 = 12)?
Is (12 = 12)? Yes
Answer: x = 27
Thanks again