# Complex Proportions

In this video, we will be learning how to solve complex proportions (variables on both sides) using cross-multiplication.

For Example:

$\frac{x}{20}=\frac{(x+1)}{30}\leftarrow$ First we cross-multiply

$30x=20(x+1)\leftarrow$ Then we distribute the 20 to the x and 1

$30x-20x=20x +20-20x\leftarrow$ Subtract 20x from both sides to isolate x

$\frac{10x}{10}=\frac{20}{10}\leftarrow$ Divide by 10 on both sides

$x=2$

## Video-Lesson Transcript

Let’s go over complex proportions.

For example:

$\dfrac{x}{20} = \dfrac{x + 1}{30}$

What makes this complex is that we have one variable on both sides of the equation.

We’re just going to do the same method which is to cross-multiply.

$x \times30 = 30x$

To solve the equation on the right, we have to distribute $20$ on each of term.

${x + 1} \times20$ $20x + 20$

Now we have

$30x = 20x + 20$

Let’s get all the variables on one side by subtracting $20x$ on both sides.

$30x - 20x = 20x - 20x + 20$ $10x = 20$

Simply solve $x$ by dividing both sides by $10$.

$\dfrac{10x}{10} = \dfrac{20}{10}$

And we’ll have

$x = 2$

Complex proportion is different from regular proportion because it has a variable on both sides of the equation.