Question

How would you solve `(x)/(2)+(x)/(3)=(5x+2)/(6)`? The hint given was multiply everything by 6.

When I multiplied by 6, the result was the 2 left over. Help?

Answer 1

This equation has `"no solution"`

Explanation:

You can clear the fractions by multiplying every term by `6` and letting the denominators cancel.

Once you get rid of the denominators by canceling them, you should have a nice, easy problem to solve.

`(x)/(2)+(x)/(3) =(5x+2)/(6)`    Solve for `x`

1) Get rid of the fractions by multiplying every term on both sides by `6` and letting the denominators cancel

`cancel ((6))(x)/ cancel(2)+ cancel((6))(x)/cancel (3) =(cancel6)(5x+2)/cancel(6)`

2) After you cancel the denominators with the `6'`s, you will get this:

`3x + 2x = 5x + 2`

`Oh  oh!`

The equation says
`5x = 5x + 2`

That simplifies to
`0 = 2`

But this is a false statement.
`0` does not equal `2`

So therefore there is `"no solution"`

Answer
There is no solution to this problem

You can read a little more about problems like this here:
http://www.charleston.k12.il.us/cms/Teachers/math/PreAlgebra/paunit5/L5-4.PDF