Solve k/2x-4-1=x/x-2

$$\frac { k } { 2 x - 4 } - 1 = \frac { x } { x - 2 }$$

Solve for k

$$k=4\left(x-1\right)$$

$$x\neq 2$$

Solution Steps

Multiply both sides of the equation by 2\left(x-2\right), the least common multiple of 2x-4,x-2.

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

Multiply 2 and -1 to get -2.

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

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

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

Add 2x to both sides.

$$k+4=2x+2x$$

Combine 2x and 2x to get 4x.

$$k+4=4x$$

Subtract 4 from both sides.

$$k=4x-4$$

Solve for x

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

$$k\neq 4$$

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 2\left(x-2\right), the least common multiple of 2x-4,x-2.

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

Multiply 2 and -1 to get -2.

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

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

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

Subtract 2x from both sides.

$$k-2x+4-2x=0$$

Combine -2x and -2x to get -4x.

$$k-4x+4=0$$

Subtract k from both sides. Anything subtracted from zero gives its negation.

$$-4x+4=-k$$

Subtract 4 from both sides.

$$-4x=-k-4$$

Divide both sides by -4.

$$\frac{-4x}{-4}=\frac{-k-4}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$x=\frac{-k-4}{-4}$$

Divide -k-4 by -4.

$$x=\frac{k}{4}+1$$

Variable x cannot be equal to 2.

$$x=\frac{k}{4}+1\text{, }x\neq 2$$