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Question 405449: How do I solve this problem:
1/3(2x-5)+2(3x+1)=3/4(x-8)
Answer by IWork4Dessert(60)   (Show Source):
You can put this solution on YOUR website! The first thing for you to do in this problem is to distribute, which is basically the "multiply" step in PEMDAS(order of operations).
Start by distributing all of your terms inside the parentheses.
2/3x-5/3+6x+2=3/4x-24/4
Now, it's always annoying to work with fractions in problems like these, so to get rid of them we want to find the LCM(least common multiple) of the factors to cancel them out.
2/3x-5/3+18/3+6/3=3/4x-24/4
If you look at the denominators of all these fractions, you'll see that they're all 3's and 4's. The LCM of 3 and 4 is 12, which means that in order to get rid of your fractions(clear them), you'll need to multiply both sides by 12.
(2/3x-5/3+18/3+6/3)12=(3/4x-24/4)12
Distribute the 12 inside both of the sets of parentheses and simplify.
24/3x-60/3+216/3+72/3=36/4x-288/4
Divide them in.
8x-20+72+24=9x-72
Now just simplify the problem further by combining your like terms.
8x+76=9x-72
Your ultimate goal in this problem is to isolate your variable(x) on one side of the equation. To do this you have to get rid of every other number around it on the left or right side of the equal sign.
Let's get the variable on the left side for example's sake.
Since the 9x on the right side is positive, subtract it from both sides of the equation to cancel it out.
-x+76=-72
Now get rid of the 76 on the left side of the equation by subtracting it from both sides.
-x=-148
You can't end with a negative variable, so divide both sides by -1 to keep it positive.
x=148
Your answer is 148.
Hope this helps!
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