Simplifying and Combining Like Terms: Solving an equation with fractions

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:

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

$\frac{21}{40}$

Solve for x:

$-\frac{1}{5}x+\frac{1}{4}x+\frac{1}{20}x-\frac{1}{5}=\frac{3}{10}-\frac{2}{5}+\frac{2}{10}x$

• Move similar terms to one side.

• Create common denominators using the least common multiple of the different fractions.

• Reduction of fractions.

-1

Solve for X:

$-\frac{1}{7}+\frac{3}{4}x=\frac{1}{8}x+\frac{3}{14}$

$\frac{8}{14}$

Solve for X:

$\frac{1}{8}x+3=-\frac{1}{5}+\frac{5}{16}x$

$\frac{256}{15}$

Solve for X:

$\frac{1}{4}+\frac{2}{5}x=-\frac{3}{4}+\frac{1}{10}x$

$-\frac{10}{3}$

Solve for X:

$-x+\frac{1}{4}-\frac{1}{3}+\frac{1}{8}=5+\frac{1}{4}x-\frac{1}{3}x$

$-\frac{119}{22}$

Solve for X:

$-\frac{1}{5}x+\frac{1}{3}-\frac{1}{4}x+1=3x-\frac{1}{5}$

$\frac{4}{9}$

Solve for X:

$-\frac{1}{5}(x+\frac{1}{5})+\frac{1}{3}=-\frac{1}{4}x+\frac{1}{5}$

$-\frac{28}{15}$

Solve for X:

$-\frac{1}{5}(x-\frac{1}{3})+\frac{1}{15}=-\frac{3}{5}x+\frac{1}{10}$

$-\frac{1}{12}$

Solve for X:

$-\frac{1}{5}(x+\frac{1}{4})=\frac{7}{10}+\frac{3}{5}x-\frac{2}{5}$

$-\frac{7}{16}$