Solve the Fraction Equation: -1/2 + (1/3)x = 1/5 + x

Solve for x:

$-\frac{1}{2}+\frac{1}{3}x=\frac{1}{5}-x$

We will move the elements with the X to the left side and the elements without the X to the right side, changing the plus and minus signs accordingly.

First, we move the minus X to the left section:

$-\frac{1}{2}+\frac{1}{3}x+x=\frac{1}{5}$

Now we move the minus 1/2 to the right section:

$\frac{1}{3}x+x=\frac{1}{5}+\frac{1}{2}$

We will find a common denominator for the fractions on the right side and reduce accordingly. Convert the mixed fraction on the left side into a simple fraction:

$1\frac{1}{3}x=\frac{2+5}{10}$

$\frac{4}{3}x=\frac{7}{10}$

Multiply by$\frac{3}{4}$ to reduce the left side:

$x=\frac{7}{10}\times\frac{3}{4}=\frac{7\times3}{10\times4}=\frac{21}{40}$