Solve 4(x/y+1)=10

$$4 ( \frac { x } { y } + 1 ) = 10$$

Solve for x

$$x=\frac{3y}{2}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Divide both sides by 4.

$$\frac{x}{y}+1=\frac{10}{4}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{x}{y}+1=\frac{5}{2}$$

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

$$2x+2y=5y$$

Subtract 2y from both sides.

$$2x=5y-2y$$

Combine 5y and -2y to get 3y.

$$2x=3y$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{3y}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{3y}{2}$$

Solve for y

$$y=\frac{2x}{3}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Divide both sides by 4.

$$\frac{x}{y}+1=\frac{10}{4}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{x}{y}+1=\frac{5}{2}$$

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2y, the least common multiple of y,2.

$$2x+2y=5y$$

Subtract 5y from both sides.

$$2x+2y-5y=0$$

Combine 2y and -5y to get -3y.

$$2x-3y=0$$

Subtract 2x from both sides. Anything subtracted from zero gives its negation.

$$-3y=-2x$$

Divide both sides by -3.

$$\frac{-3y}{-3}=-\frac{2x}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$y=-\frac{2x}{-3}$$

Divide -2x by -3.

$$y=\frac{2x}{3}$$

Variable y cannot be equal to 0.

$$y=\frac{2x}{3}\text{, }y\neq 0$$