Solve 3(1/3+x/5)-2/3=1/5(2x-frac{1}{3})

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

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 3,5.

$$45\left(\frac{1}{3}+\frac{x}{5}\right)-10=3\left(2x-\frac{1}{3}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 5 is 15. Multiply \frac{1}{3} times \frac{5}{5}. Multiply \frac{x}{5} times \frac{3}{3}.

$$45\left(\frac{5}{15}+\frac{3x}{15}\right)-10=3\left(2x-\frac{1}{3}\right)$$

Since \frac{5}{15} and \frac{3x}{15} have the same denominator, add them by adding their numerators.

$$45\times \frac{5+3x}{15}-10=3\left(2x-\frac{1}{3}\right)$$

Cancel out 15, the greatest common factor in 45 and 15.

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

Use the distributive property to multiply 3 by 5+3x.

$$15+9x-10=3\left(2x-\frac{1}{3}\right)$$

Subtract 10 from 15 to get 5.

$$5+9x=3\left(2x-\frac{1}{3}\right)$$

Use the distributive property to multiply 3 by 2x-\frac{1}{3}.

$$5+9x=6x+3\left(-\frac{1}{3}\right)$$

Cancel out 3 and 3.

$$5+9x=6x-1$$

Subtract 6x from both sides.

$$5+9x-6x=-1$$

Combine 9x and -6x to get 3x.

$$5+3x=-1$$

Subtract 5 from both sides.

$$3x=-1-5$$

Subtract 5 from -1 to get -6.

$$3x=-6$$

Divide both sides by 3.

$$x=\frac{-6}{3}$$

Divide -6 by 3 to get -2.

$$x=-2$$