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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.