Solve x-1/2+1/3*-3(x-2)/6=x+4/4

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

Solve for x

$$x=14$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 2,3,6,4.

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

Use the distributive property to multiply 6 by x-1.

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

Use the distributive property to multiply 3 by x-2.

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

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

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

Use the distributive property to multiply 3 by x+4.

$$6x-6+\frac{-4\left(3x-6\right)}{6}=3x+12$$

Divide -4\left(3x-6\right) by 6 to get -\frac{2}{3}\left(3x-6\right).

$$6x-6-\frac{2}{3}\left(3x-6\right)=3x+12$$

Use the distributive property to multiply -\frac{2}{3} by 3x-6.

$$6x-6-\frac{2}{3}\times 3x-\frac{2}{3}\left(-6\right)=3x+12$$

Cancel out 3 and 3.

$$6x-6-2x-\frac{2}{3}\left(-6\right)=3x+12$$

Express -\frac{2}{3}\left(-6\right) as a single fraction.

$$6x-6-2x+\frac{-2\left(-6\right)}{3}=3x+12$$

Multiply -2 and -6 to get 12.

$$6x-6-2x+\frac{12}{3}=3x+12$$

Divide 12 by 3 to get 4.

$$6x-6-2x+4=3x+12$$

Combine 6x and -2x to get 4x.

$$4x-6+4=3x+12$$

Add -6 and 4 to get -2.

$$4x-2=3x+12$$

Subtract 3x from both sides.

$$4x-2-3x=12$$

Combine 4x and -3x to get x.

$$x-2=12$$

Add 2 to both sides.

$$x=12+2$$

Add 12 and 2 to get 14.

$$x=14$$