Solve 1/2(x-3)-1/3(x+2)=x

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

Solve for x

$$x = -\frac{13}{5} = -2\frac{3}{5} = -2.6$$

Steps for Solving Linear Equation

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

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

Multiply \frac{1}{2} and -3 to get \frac{-3}{2}.

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

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

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

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

$$\frac{1}{2}x-\frac{3}{2}-\frac{1}{3}x-\frac{1}{3}\times 2=x$$

Express -\frac{1}{3}\times 2 as a single fraction.

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

Combine \frac{1}{2}x and -\frac{1}{3}x to get \frac{1}{6}x.

$$\frac{1}{6}x-\frac{3}{2}-\frac{2}{3}=x$$

Least common multiple of 2 and 3 is 6. Convert -\frac{3}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{1}{6}x-\frac{9}{6}-\frac{4}{6}=x$$

Since -\frac{9}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{6}x+\frac{-9-4}{6}=x$$

Subtract 4 from -9 to get -13.

$$\frac{1}{6}x-\frac{13}{6}=x$$

Subtract x from both sides.

$$\frac{1}{6}x-\frac{13}{6}-x=0$$

Combine \frac{1}{6}x and -x to get -\frac{5}{6}x.

$$-\frac{5}{6}x-\frac{13}{6}=0$$

Add \frac{13}{6} to both sides. Anything plus zero gives itself.

$$-\frac{5}{6}x=\frac{13}{6}$$

Multiply both sides by -\frac{6}{5}, the reciprocal of -\frac{5}{6}.

$$x=\frac{13}{6}\left(-\frac{6}{5}\right)$$

Multiply \frac{13}{6} times -\frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{13\left(-6\right)}{6\times 5}$$

Do the multiplications in the fraction \frac{13\left(-6\right)}{6\times 5}.

$$x=\frac{-78}{30}$$

Reduce the fraction \frac{-78}{30} to lowest terms by extracting and canceling out 6.

$$x=-\frac{13}{5}$$