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