Solve 3+2x/5-(2-3-x/3)=x

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

Solve for x

$$x=-\frac{3}{7}\approx -0.428571429$$

Steps for Solving Linear Equation

To find the opposite of 2-\frac{3-x}{3}, find the opposite of each term.

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

Divide each term of 3+2x by 5 to get \frac{3}{5}+\frac{2}{5}x.

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

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

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

Since \frac{3}{5} and \frac{10}{5} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 10 from 3 to get -7.

$$-\frac{7}{5}+\frac{2}{5}x-\left(-\frac{3-x}{3}\right)=x$$

Divide each term of 3-x by 3 to get 1-\frac{1}{3}x.

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

To find the opposite of 1-\frac{1}{3}x, find the opposite of each term.

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

The opposite of -\frac{1}{3}x is \frac{1}{3}x.

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

To find the opposite of -1+\frac{1}{3}x, find the opposite of each term.

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

The opposite of -1 is 1.

$$-\frac{7}{5}+\frac{2}{5}x+1-\frac{1}{3}x=x$$

Convert 1 to fraction \frac{5}{5}.

$$-\frac{7}{5}+\frac{2}{5}x+\frac{5}{5}-\frac{1}{3}x=x$$

Since -\frac{7}{5} and \frac{5}{5} have the same denominator, add them by adding their numerators.

$$\frac{-7+5}{5}+\frac{2}{5}x-\frac{1}{3}x=x$$

Add -7 and 5 to get -2.

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

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

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

Subtract x from both sides.

$$-\frac{2}{5}+\frac{1}{15}x-x=0$$

Combine \frac{1}{15}x and -x to get -\frac{14}{15}x.

$$-\frac{2}{5}-\frac{14}{15}x=0$$

Add \frac{2}{5} to both sides. Anything plus zero gives itself.

$$-\frac{14}{15}x=\frac{2}{5}$$

Multiply both sides by -\frac{15}{14}, the reciprocal of -\frac{14}{15}.

$$x=\frac{2}{5}\left(-\frac{15}{14}\right)$$

Multiply \frac{2}{5} times -\frac{15}{14} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{2\left(-15\right)}{5\times 14}$$

Do the multiplications in the fraction \frac{2\left(-15\right)}{5\times 14}.

$$x=\frac{-30}{70}$$

Reduce the fraction \frac{-30}{70} to lowest terms by extracting and canceling out 10.

$$x=-\frac{3}{7}$$