Solve 1/2left(x-1right)-1/3left(3x-6right)=1/4left(2x-8right)

$$\frac{ 1 }{ 2 } \left( x-1 \right) - \frac{ 1 }{ 3 } \left( 3x-6 \right) = \frac{ 1 }{ 4 } \left( 2x-8 \right)$$

Solve for x

$$x = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

Steps for Solving Linear Equation

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

$$\frac{1}{2}x+\frac{1}{2}\left(-1\right)-\frac{1}{3}\left(3x-6\right)=\frac{1}{4}\left(2x-8\right)$$

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

$$\frac{1}{2}x-\frac{1}{2}-\frac{1}{3}\left(3x-6\right)=\frac{1}{4}\left(2x-8\right)$$

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

$$\frac{1}{2}x-\frac{1}{2}-\frac{1}{3}\times 3x-\frac{1}{3}\left(-6\right)=\frac{1}{4}\left(2x-8\right)$$

Cancel out 3 and 3.

$$\frac{1}{2}x-\frac{1}{2}-x-\frac{1}{3}\left(-6\right)=\frac{1}{4}\left(2x-8\right)$$

Express -\frac{1}{3}\left(-6\right) as a single fraction.

$$\frac{1}{2}x-\frac{1}{2}-x+\frac{-\left(-6\right)}{3}=\frac{1}{4}\left(2x-8\right)$$

Multiply -1 and -6 to get 6.

$$\frac{1}{2}x-\frac{1}{2}-x+\frac{6}{3}=\frac{1}{4}\left(2x-8\right)$$

Divide 6 by 3 to get 2.

$$\frac{1}{2}x-\frac{1}{2}-x+2=\frac{1}{4}\left(2x-8\right)$$

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

$$-\frac{1}{2}x-\frac{1}{2}+2=\frac{1}{4}\left(2x-8\right)$$

Convert 2 to fraction \frac{4}{2}.

$$-\frac{1}{2}x-\frac{1}{2}+\frac{4}{2}=\frac{1}{4}\left(2x-8\right)$$

Since -\frac{1}{2} and \frac{4}{2} have the same denominator, add them by adding their numerators.

$$-\frac{1}{2}x+\frac{-1+4}{2}=\frac{1}{4}\left(2x-8\right)$$

Add -1 and 4 to get 3.

$$-\frac{1}{2}x+\frac{3}{2}=\frac{1}{4}\left(2x-8\right)$$

Use the distributive property to multiply \frac{1}{4} by 2x-8.

$$-\frac{1}{2}x+\frac{3}{2}=\frac{1}{4}\times 2x+\frac{1}{4}\left(-8\right)$$

Multiply \frac{1}{4} and 2 to get \frac{2}{4}.

$$-\frac{1}{2}x+\frac{3}{2}=\frac{2}{4}x+\frac{1}{4}\left(-8\right)$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{2}x+\frac{3}{2}=\frac{1}{2}x+\frac{1}{4}\left(-8\right)$$

Multiply \frac{1}{4} and -8 to get \frac{-8}{4}.

$$-\frac{1}{2}x+\frac{3}{2}=\frac{1}{2}x+\frac{-8}{4}$$

Divide -8 by 4 to get -2.

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

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

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

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

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

Subtract \frac{3}{2} from both sides.

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

Convert -2 to fraction -\frac{4}{2}.

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

Since -\frac{4}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from -4 to get -7.

$$-x=-\frac{7}{2}$$

Multiply both sides by -1.

$$x=\frac{7}{2}$$