Solve 1/3(x-6)-1/5(2x-3)=-4/15x

$$\frac { 1 } { 3 } ( x - 6 ) - \frac { 1 } { 5 } ( 2 x - 3 ) = - \frac { 4 } { 15 } x$$

Solve for x

$$x=7$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by x-6.

$$\frac{1}{3}x+\frac{1}{3}\left(-6\right)-\frac{1}{5}\left(2x-3\right)=-\frac{4}{15}x$$

Multiply \frac{1}{3} and -6 to get \frac{-6}{3}.

$$\frac{1}{3}x+\frac{-6}{3}-\frac{1}{5}\left(2x-3\right)=-\frac{4}{15}x$$

Divide -6 by 3 to get -2.

$$\frac{1}{3}x-2-\frac{1}{5}\left(2x-3\right)=-\frac{4}{15}x$$

Use the distributive property to multiply -\frac{1}{5} by 2x-3.

$$\frac{1}{3}x-2-\frac{1}{5}\times 2x-\frac{1}{5}\left(-3\right)=-\frac{4}{15}x$$

Express -\frac{1}{5}\times 2 as a single fraction.

$$\frac{1}{3}x-2+\frac{-2}{5}x-\frac{1}{5}\left(-3\right)=-\frac{4}{15}x$$

Fraction \frac{-2}{5} can be rewritten as -\frac{2}{5} by extracting the negative sign.

$$\frac{1}{3}x-2-\frac{2}{5}x-\frac{1}{5}\left(-3\right)=-\frac{4}{15}x$$

Express -\frac{1}{5}\left(-3\right) as a single fraction.

$$\frac{1}{3}x-2-\frac{2}{5}x+\frac{-\left(-3\right)}{5}=-\frac{4}{15}x$$

Multiply -1 and -3 to get 3.

$$\frac{1}{3}x-2-\frac{2}{5}x+\frac{3}{5}=-\frac{4}{15}x$$

Combine \frac{1}{3}x and -\frac{2}{5}x to get -\frac{1}{15}x.

$$-\frac{1}{15}x-2+\frac{3}{5}=-\frac{4}{15}x$$

Convert -2 to fraction -\frac{10}{5}.

$$-\frac{1}{15}x-\frac{10}{5}+\frac{3}{5}=-\frac{4}{15}x$$

Since -\frac{10}{5} and \frac{3}{5} have the same denominator, add them by adding their numerators.

$$-\frac{1}{15}x+\frac{-10+3}{5}=-\frac{4}{15}x$$

Add -10 and 3 to get -7.

$$-\frac{1}{15}x-\frac{7}{5}=-\frac{4}{15}x$$

Add \frac{4}{15}x to both sides.

$$-\frac{1}{15}x-\frac{7}{5}+\frac{4}{15}x=0$$

Combine -\frac{1}{15}x and \frac{4}{15}x to get \frac{1}{5}x.

$$\frac{1}{5}x-\frac{7}{5}=0$$

Add \frac{7}{5} to both sides. Anything plus zero gives itself.

$$\frac{1}{5}x=\frac{7}{5}$$

Multiply both sides by 5, the reciprocal of \frac{1}{5}.

$$x=\frac{7}{5}\times 5$$

Cancel out 5 and 5.

$$x=7$$