Solve 2x-6/6-x+9/7=x-12

$$\frac { 2 x - 6 } { 6 } - \frac { x + 9 } { 7 } = x - 12$$

Solve for x

$$x=12$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 42, the least common multiple of 6,7.

$$7\left(2x-6\right)-6\left(x+9\right)=42x-504$$

Use the distributive property to multiply 7 by 2x-6.

$$14x-42-6\left(x+9\right)=42x-504$$

Use the distributive property to multiply -6 by x+9.

$$14x-42-6x-54=42x-504$$

Combine 14x and -6x to get 8x.

$$8x-42-54=42x-504$$

Subtract 54 from -42 to get -96.

$$8x-96=42x-504$$

Subtract 42x from both sides.

$$8x-96-42x=-504$$

Combine 8x and -42x to get -34x.

$$-34x-96=-504$$

Add 96 to both sides.

$$-34x=-504+96$$

Add -504 and 96 to get -408.

$$-34x=-408$$

Divide both sides by -34.

$$x=\frac{-408}{-34}$$

Divide -408 by -34 to get 12.

$$x=12$$