Solve k/x-3+2=4-x/x-3

$$\frac { k } { x - 3 } + 2 = \frac { 4 - x } { x - 3 }$$

Solve for k

$$k=10-3x$$

$$x\neq 3$$

Solution Steps

Multiply both sides of the equation by x-3.

$$k+\left(x-3\right)\times 2=4-x$$

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

$$k+2x-6=4-x$$

Subtract 2x from both sides.

$$k-6=4-x-2x$$

Combine -x and -2x to get -3x.

$$k-6=4-3x$$

Add 6 to both sides.

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

Add 4 and 6 to get 10.

$$k=10-3x$$

Solve for x

$$x=\frac{10-k}{3}$$

$$k\neq 1$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by x-3.

$$k+\left(x-3\right)\times 2=4-x$$

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

$$k+2x-6=4-x$$

Add x to both sides.

$$k+2x-6+x=4$$

Combine 2x and x to get 3x.

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

Subtract k from both sides.

$$3x-6=4-k$$

Add 6 to both sides.

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

Add 4 and 6 to get 10.

$$3x=10-k$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{10-k}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{10-k}{3}$$

Variable x cannot be equal to 3.

$$x=\frac{10-k}{3}\text{, }x\neq 3$$