Question 1067145: How do I write an equivalent equation that does not contain fractions and solve: 2/3x + 1 = 1/2?
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! How do I write an equivalent equation that does not contain fractions and solve: 2/3x + 1 = 1/2?
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I'm assuming the equation is (2/3)x + 1 = 1/2 (parenthesis are important)
You need to find a common denominator and then multiply both sides of the equation by that number. You can do practically anything you want to one side of the equation as long as you also do it to the other side as well (example: if x=2, then x+4 = 2+4, or 100x = 100*2, or x/10 = 2/10, etc.).
A common denominator will be 2*3 = 6 (this is the easiest way to find a common denominator, multiply all the denominators together and works well for small sets of numbers).
We multiply both sides by 6:
On the left, the 6 multiplies into the parenthesis by the distributive property of multiplication, while on the right we just get the number 3:
 <<< equivalent equation with no fractions, 6*(2/3) is 4
 <<< subtract 6 from both sides of equation
 <<< divided both sides by 4
The answer is a fraction, not much you can do about that. You could write it as decimal if you want, in that case x = -0.75. (Fractions indicate division, so -3/4 is literally "-3 divided by 4")
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