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

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

Solve for x

$$x=-11$$

Steps for Solving Linear Equation

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

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

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

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

Convert 1 to fraction \frac{3}{3}.

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

Since -\frac{1}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from -1 to get -4.

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

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

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

Subtract \frac{1}{2}x from both sides.

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

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

$$-\frac{1}{6}x-\frac{4}{3}=\frac{1}{2}$$

Add \frac{4}{3} to both sides.

$$-\frac{1}{6}x=\frac{1}{2}+\frac{4}{3}$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{4}{3} to fractions with denominator 6.

$$-\frac{1}{6}x=\frac{3}{6}+\frac{8}{6}$$

Since \frac{3}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$-\frac{1}{6}x=\frac{3+8}{6}$$

Add 3 and 8 to get 11.

$$-\frac{1}{6}x=\frac{11}{6}$$

Multiply both sides by -6, the reciprocal of -\frac{1}{6}.

$$x=\frac{11}{6}\left(-6\right)$$

Express \frac{11}{6}\left(-6\right) as a single fraction.

$$x=\frac{11\left(-6\right)}{6}$$

Multiply 11 and -6 to get -66.

$$x=\frac{-66}{6}$$

Divide -66 by 6 to get -11.

$$x=-11$$