Question 23286: -1/2+3z=1/2z+2/3 please help me..i have trouble solving fractions..thank you..
Answer by smik(40)   (Show Source):
You can put this solution on YOUR website! Okay, the key to solving anything with one variable (in this case the 'z') is to isolate the variable. In other words, you must shift the variable to one side, and the constant to the other side. We have: -1/2 + 3z = 1/2z + 2/3.
We can start off by shifting the '1/2z' to the left side, which means we subtract it from the right side and do the same on the left. We subtract 1/2z by itself and get 0z on the right side. We subtract 3z by 1/2z on the left side and get 2.5z, or 5/2z (in fraction form). So we have:
-1/2 + 5/2z = 2/3
Now, we can shift the -1/2 on the left hand side to the right hand side, by adding 1/2 on each side. We add 1/2 to (-1/2) on the left and get 0. We add 2/3 and 1/2 on the right and get 7/6 on the right. So we have:
5/2z = 7/6
Now we just divide 7/6 by 5/2. This is the same as multiplying 7/6 by 2/5. And if we multiply 7/6 by 2/5 we get (7*2)/(5*6) which is 14/30. So the final answer is:
z = 14/30
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