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

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

Solve for x

$$x=0$$

Steps for Solving Linear Equation

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

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

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

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

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

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

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

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

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

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

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

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

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

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

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

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

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

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

Subtract \frac{1}{2} from \frac{1}{2} to get 0.

$$-\frac{1}{3}x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -\frac{1}{3} is not equal to 0, x must be equal to 0.

$$x=0$$