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

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

Solve for k

$$k=5-2x$$

$$x\neq 2$$

Solution Steps

Multiply both sides of the equation by x-2, the least common multiple of x-2,2-x.

$$k+\left(x-2\right)\times 3=-\left(1-x\right)$$

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

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

To find the opposite of 1-x, find the opposite of each term.

$$k+3x-6=-1+x$$

Subtract 3x from both sides.

$$k-6=-1+x-3x$$

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

$$k-6=-1-2x$$

Add 6 to both sides.

$$k=-1-2x+6$$

Add -1 and 6 to get 5.

$$k=5-2x$$

Solve for x

$$x=\frac{5-k}{2}$$

$$k\neq 1$$

Steps for Solving Linear Equation

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by x-2, the least common multiple of x-2,2-x.

$$k+\left(x-2\right)\times 3=-\left(1-x\right)$$

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

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

To find the opposite of 1-x, find the opposite of each term.

$$k+3x-6=-1+x$$

Subtract x from both sides.

$$k+3x-6-x=-1$$

Combine 3x and -x to get 2x.

$$k+2x-6=-1$$

Subtract k from both sides.

$$2x-6=-1-k$$

Add 6 to both sides.

$$2x=-1-k+6$$

Add -1 and 6 to get 5.

$$2x=5-k$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{5-k}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{5-k}{2}$$

Variable x cannot be equal to 2.

$$x=\frac{5-k}{2}\text{, }x\neq 2$$