Solve y=7/-x-6

$$y = \frac { 7 } { - x } - 6$$

Solve for x

$$x=-\frac{7}{y+6}$$

$$y\neq -6$$

Steps for Solving Linear Equation

Factor -x.

$$y=\frac{7}{-x}-6$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{-x}{-x}.

$$y=\frac{7}{-x}-\frac{6\left(-1\right)x}{-x}$$

Since \frac{7}{-x} and \frac{6\left(-1\right)x}{-x} have the same denominator, subtract them by subtracting their numerators.

$$y=\frac{7-6\left(-1\right)x}{-x}$$

Do the multiplications in 7-6\left(-1\right)x.

$$y=\frac{7+6x}{-x}$$

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

$$\frac{7+6x}{-x}=y$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$-\left(7+6x\right)=yx$$

To find the opposite of 7+6x, find the opposite of each term.

$$-7-6x=yx$$

Subtract yx from both sides.

$$-7-6x-yx=0$$

Add 7 to both sides. Anything plus zero gives itself.

$$-6x-yx=7$$

Combine all terms containing x.

$$\left(-6-y\right)x=7$$

The equation is in standard form.

$$\left(-y-6\right)x=7$$

Divide both sides by -6-y.

$$\frac{\left(-y-6\right)x}{-y-6}=\frac{7}{-y-6}$$

Dividing by -6-y undoes the multiplication by -6-y.

$$x=\frac{7}{-y-6}$$

Divide 7 by -6-y.

$$x=-\frac{7}{y+6}$$

Variable x cannot be equal to 0.

$$x=-\frac{7}{y+6}\text{, }x\neq 0$$

Solve for y

$$y=-6-\frac{7}{x}$$

$$x\neq 0$$