Solve y=a/x-6+4

$$y = \frac { a } { x - 6 } + 4$$

Solve for a

$$a=-\left(6-x\right)\left(y-4\right)$$

$$x\neq 6$$

Solution Steps

Multiply both sides of the equation by x-6.

$$y\left(x-6\right)=a+\left(x-6\right)\times 4$$

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

$$yx-6y=a+\left(x-6\right)\times 4$$

Use the distributive property to multiply x-6 by 4.

$$yx-6y=a+4x-24$$

Swap sides so that all variable terms are on the left hand side.

$$a+4x-24=yx-6y$$

Subtract 4x from both sides.

$$a-24=yx-6y-4x$$

Add 24 to both sides.

$$a=yx-6y-4x+24$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{6y+a-24}{4-y}\text{, }&a\neq 0\text{ and }y\neq 4\\x\neq 6\text{, }&y=4\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable x cannot be equal to 6 since division by zero is not defined. Multiply both sides of the equation by x-6.

$$y\left(x-6\right)=a+\left(x-6\right)\times 4$$

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

$$yx-6y=a+\left(x-6\right)\times 4$$

Use the distributive property to multiply x-6 by 4.

$$yx-6y=a+4x-24$$

Subtract 4x from both sides.

$$yx-6y-4x=a-24$$

Add 6y to both sides.

$$yx-4x=a-24+6y$$

Combine all terms containing x.

$$\left(y-4\right)x=a-24+6y$$

The equation is in standard form.

$$\left(y-4\right)x=6y+a-24$$

Divide both sides by y-4.

$$\frac{\left(y-4\right)x}{y-4}=\frac{6y+a-24}{y-4}$$

Dividing by y-4 undoes the multiplication by y-4.

$$x=\frac{6y+a-24}{y-4}$$

Variable x cannot be equal to 6.

$$x=\frac{6y+a-24}{y-4}\text{, }x\neq 6$$