Solve 3x-6/k+2x-9/6=x/3

$$\frac { 3 x - 6 } { k } + \frac { 2 x - 9 } { 6 } = \frac { x } { 3 }$$

Solve for k

$$k=2\left(x-2\right)$$

$$x\neq 2$$

Steps for Solving Linear Equation

Variable k cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6k, the least common multiple of k,6,3.

$$6\left(3x-6\right)+k\left(2x-9\right)=2kx$$

Use the distributive property to multiply 6 by 3x-6.

$$18x-36+k\left(2x-9\right)=2kx$$

Use the distributive property to multiply k by 2x-9.

$$18x-36+2kx-9k=2kx$$

Subtract 2kx from both sides.

$$18x-36+2kx-9k-2kx=0$$

Combine 2kx and -2kx to get 0.

$$18x-36-9k=0$$

Subtract 18x from both sides. Anything subtracted from zero gives its negation.

$$-36-9k=-18x$$

Add 36 to both sides.

$$-9k=-18x+36$$

The equation is in standard form.

$$-9k=36-18x$$

Divide both sides by -9.

$$\frac{-9k}{-9}=\frac{36-18x}{-9}$$

Dividing by -9 undoes the multiplication by -9.

$$k=\frac{36-18x}{-9}$$

Divide -18x+36 by -9.

$$k=2x-4$$

Variable k cannot be equal to 0.

$$k=2x-4\text{, }k\neq 0$$

Solve for x

$$x=\frac{k+4}{2}$$

$$k\neq 0$$

Steps for Solving Linear Equation

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

$$6\left(3x-6\right)+k\left(2x-9\right)=2kx$$

Use the distributive property to multiply 6 by 3x-6.

$$18x-36+k\left(2x-9\right)=2kx$$

Use the distributive property to multiply k by 2x-9.

$$18x-36+2kx-9k=2kx$$

Subtract 2kx from both sides.

$$18x-36+2kx-9k-2kx=0$$

Combine 2kx and -2kx to get 0.

$$18x-36-9k=0$$

Add 36 to both sides. Anything plus zero gives itself.

$$18x-9k=36$$

Add 9k to both sides.

$$18x=36+9k$$

The equation is in standard form.

$$18x=9k+36$$

Divide both sides by 18.

$$\frac{18x}{18}=\frac{9k+36}{18}$$

Dividing by 18 undoes the multiplication by 18.

$$x=\frac{9k+36}{18}$$

Divide 36+9k by 18.

$$x=\frac{k}{2}+2$$