Solve y=(7-x)(2y+1)/x

$$y = \frac { ( 7 - x ) ( 2 y + 1 ) } { x }$$

Solve for x

$$x=\frac{7\left(2y+1\right)}{3y+1}$$

$$y\neq -\frac{1}{2}\text{ and }y\neq -\frac{1}{3}$$

Steps for Solving Linear Equation

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

$$yx=\left(7-x\right)\left(2y+1\right)$$

Use the distributive property to multiply 7-x by 2y+1.

$$yx=14y+7-2yx-x$$

Add 2yx to both sides.

$$yx+2yx=14y+7-x$$

Combine yx and 2yx to get 3yx.

$$3yx=14y+7-x$$

Add x to both sides.

$$3yx+x=14y+7$$

Combine all terms containing x.

$$\left(3y+1\right)x=14y+7$$

Divide both sides by 3y+1.

$$\frac{\left(3y+1\right)x}{3y+1}=\frac{14y+7}{3y+1}$$

Dividing by 3y+1 undoes the multiplication by 3y+1.

$$x=\frac{14y+7}{3y+1}$$

Divide 14y+7 by 3y+1.

$$x=\frac{7\left(2y+1\right)}{3y+1}$$

Variable x cannot be equal to 0.

$$x=\frac{7\left(2y+1\right)}{3y+1}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{x-7}{3x-14}$$

$$x\neq \frac{14}{3}\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 7-x by 2y+1.

$$y=\frac{14y+7-2yx-x}{x}$$

Subtract \frac{14y+7-2yx-x}{x} from both sides.

$$y-\frac{14y+7-2yx-x}{x}=0$$

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

$$\frac{yx}{x}-\frac{14y+7-2yx-x}{x}=0$$

Since \frac{yx}{x} and \frac{14y+7-2yx-x}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{yx-\left(14y+7-2yx-x\right)}{x}=0$$

Do the multiplications in yx-\left(14y+7-2yx-x\right).

$$\frac{yx-14y-7+2xy+x}{x}=0$$

Combine like terms in yx-14y-7+2xy+x.

$$\frac{-7+3yx+x-14y}{x}=0$$

Multiply both sides of the equation by x.

$$-7+3yx+x-14y=0$$

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

$$3yx+x-14y=7$$

Subtract x from both sides.

$$3yx-14y=7-x$$

Combine all terms containing y.

$$\left(3x-14\right)y=7-x$$

Divide both sides by 3x-14.

$$\frac{\left(3x-14\right)y}{3x-14}=\frac{7-x}{3x-14}$$

Dividing by 3x-14 undoes the multiplication by 3x-14.

$$y=\frac{7-x}{3x-14}$$