# 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?

Mar 8, 2018

This equation has $\text{no solution}$

#### 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.

$\frac{x}{2} + \frac{x}{3} = \frac{5 x + 2}{6}$    Solve for $x$

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

$\cancel{\left(6\right)} \frac{x}{\cancel{2}} + \cancel{\left(6\right)} \frac{x}{\cancel{3}} = \left(\cancel{6}\right) \frac{5 x + 2}{\cancel{6}}$

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

$3 x + 2 x = 5 x + 2$

Oh  oh!

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

That simplifies to
$0 = 2$

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

So therefore there is $\text{no solution}$