Solve frac{sqrt{3}}{3}=y+24/x

$$\frac { \sqrt { 3 } } { 3 } = \frac { y + 24 } { x }$$

Solve for x

$$x=\sqrt{3}\left(y+24\right)$$

$$y\neq -24$$

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 3x, the least common multiple of 3,x.

$$x\sqrt{3}=3\left(y+24\right)$$

Use the distributive property to multiply 3 by y+24.

$$x\sqrt{3}=3y+72$$

The equation is in standard form.

$$\sqrt{3}x=3y+72$$

Divide both sides by \sqrt{3}.

$$\frac{\sqrt{3}x}{\sqrt{3}}=\frac{3y+72}{\sqrt{3}}$$

Dividing by \sqrt{3} undoes the multiplication by \sqrt{3}.

$$x=\frac{3y+72}{\sqrt{3}}$$

Divide 72+3y by \sqrt{3}.

$$x=\sqrt{3}\left(y+24\right)$$

Variable x cannot be equal to 0.

$$x=\sqrt{3}\left(y+24\right)\text{, }x\neq 0$$

Solve for y

$$y=\frac{\sqrt{3}x-72}{3}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3x, the least common multiple of 3,x.

$$x\sqrt{3}=3\left(y+24\right)$$

Use the distributive property to multiply 3 by y+24.

$$x\sqrt{3}=3y+72$$

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

$$3y+72=x\sqrt{3}$$

Subtract 72 from both sides.

$$3y=x\sqrt{3}-72$$

The equation is in standard form.

$$3y=\sqrt{3}x-72$$

Divide both sides by 3.

$$\frac{3y}{3}=\frac{\sqrt{3}x-72}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$y=\frac{\sqrt{3}x-72}{3}$$

Divide x\sqrt{3}-72 by 3.

$$y=\frac{\sqrt{3}x}{3}-24$$