Solve x-1/2-x+2/3=x-12

$$\frac { x - 1 } { 2 } - \frac { x + 2 } { 3 } = x - 12$$

Solve for x

$$x=13$$

Steps for Solving Linear Equation

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

$$3\left(x-1\right)-2\left(x+2\right)=6x-72$$

Use the distributive property to multiply 3 by x-1.

$$3x-3-2\left(x+2\right)=6x-72$$

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

$$3x-3-2x-4=6x-72$$

Combine 3x and -2x to get x.

$$x-3-4=6x-72$$

Subtract 4 from -3 to get -7.

$$x-7=6x-72$$

Subtract 6x from both sides.

$$x-7-6x=-72$$

Combine x and -6x to get -5x.

$$-5x-7=-72$$

Add 7 to both sides.

$$-5x=-72+7$$

Add -72 and 7 to get -65.

$$-5x=-65$$

Divide both sides by -5.

$$x=\frac{-65}{-5}$$

Divide -65 by -5 to get 13.

$$x=13$$