Solve x-2/3-12-x/2=5x-36/4-1

$$\frac { x - 2 } { 3 } - \frac { 12 - x } { 2 } = \frac { 5 x - 36 } { 4 } - 1$$

Solve for x

$$x=8$$

Steps for Solving Linear Equation

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

$$4\left(x-2\right)-6\left(12-x\right)=3\left(5x-36\right)-12$$

Use the distributive property to multiply 4 by x-2.

$$4x-8-6\left(12-x\right)=3\left(5x-36\right)-12$$

Use the distributive property to multiply -6 by 12-x.

$$4x-8-72+6x=3\left(5x-36\right)-12$$

Subtract 72 from -8 to get -80.

$$4x-80+6x=3\left(5x-36\right)-12$$

Combine 4x and 6x to get 10x.

$$10x-80=3\left(5x-36\right)-12$$

Use the distributive property to multiply 3 by 5x-36.

$$10x-80=15x-108-12$$

Subtract 12 from -108 to get -120.

$$10x-80=15x-120$$

Subtract 15x from both sides.

$$10x-80-15x=-120$$

Combine 10x and -15x to get -5x.

$$-5x-80=-120$$

Add 80 to both sides.

$$-5x=-120+80$$

Add -120 and 80 to get -40.

$$-5x=-40$$

Divide both sides by -5.

$$x=\frac{-40}{-5}$$

Divide -40 by -5 to get 8.

$$x=8$$