
Robert C. answered 09/27/12
Dr. Robert can help you with Math and Science
x/2+x/3=7
The general strategy is to get rid of those denominators altogether so that the x terms can be collected on one side of the equation. What you are looking for is the lowest common multiple (LCM) of the denominators, 2 and 3. If you cannot figure out the lowest common multiple, any multiple of the denominators will do.
For example, the LCM of 2 and 3 is 6. That is, 6 is a multiple of 2 and 6 is a multiple of 3, and it is the lowest multiple that 2 and 3 share.
Multiply both sides by the LCM
6*(x/2+x/3)=6 *7 (using * as multiplication)
Distribute the 6 over each term inside the parentheses
6x/2+6x/3=42
Reduce each fraction
(6/2)x +(6/3)x = 42
3x +2x = 42
Combine like terms.
5x = 42
Divide both sides by 5
x=42/5
Now if you had used another multiple of 2 and 3 instead of 6, it would work too. Try it with 12 or 18 or 24, all multiples of 2 and 3, and you will see that it is workable.


Robert C.
Absolutely right, Fred. LCM is the way to go.
10/18/12
FREDERICK S.
Yes, Robert, any multiple will work but the LCM is most efficient and they all should learn that concept, right? But I voted for your answer as best explanation.
- a PhD in math and long-time teacher of it, Fred S
10/18/12