Solve 1/2(x-1)-1/3(x+3)=1/6

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

Solve for x

$$x=10$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Cancel out 3 and 3.

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

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

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

Convert 1 to fraction \frac{2}{2}.

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

Since -\frac{1}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from -1 to get -3.

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

Add \frac{3}{2} to both sides.

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

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

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

Since \frac{1}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

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

Add 1 and 9 to get 10.

$$\frac{1}{6}x=\frac{10}{6}$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{6}x=\frac{5}{3}$$

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

$$x=\frac{5}{3}\times 6$$

Express \frac{5}{3}\times 6 as a single fraction.

$$x=\frac{5\times 6}{3}$$

Multiply 5 and 6 to get 30.

$$x=\frac{30}{3}$$

Divide 30 by 3 to get 10.

$$x=10$$