Solve -1/4(x-8)+1/2(x+2)=x-3

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

Solve for x

$$x=8$$

Steps for Solving Linear Equation

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

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

Express -\frac{1}{4}\left(-8\right) as a single fraction.

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

Multiply -1 and -8 to get 8.

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

Divide 8 by 4 to get 2.

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

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

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

Cancel out 2 and 2.

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

Combine -\frac{1}{4}x and \frac{1}{2}x to get \frac{1}{4}x.

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

Add 2 and 1 to get 3.

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

Subtract x from both sides.

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

Combine \frac{1}{4}x and -x to get -\frac{3}{4}x.

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

Subtract 3 from both sides.

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

Subtract 3 from -3 to get -6.

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

Multiply both sides by -\frac{4}{3}, the reciprocal of -\frac{3}{4}.

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

Express -6\left(-\frac{4}{3}\right) as a single fraction.

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

Multiply -6 and -4 to get 24.

$$x=\frac{24}{3}$$

Divide 24 by 3 to get 8.

$$x=8$$