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?

1 Answer
Mar 8, 2018

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