 This video is called Solving Proportions. When you look at this problem, I see a fraction 5 over 6, and I see that it's equal to a fraction 3x minus 1 over 3x plus 6. What we're going to try to do is figure out what x has to be, so the fraction on the right is equivalent to the fraction on the left. What do I mean by equivalent? Well, what are some things that would be equivalent to one-half? It could be two-fourths, three over six, four over eight. It could be 50 over 100. What are some things that are equivalent to five-sixths? Well, if you multiply the top and the bottom times two, you could have 10-12ths. You could have 15-18ths. If you multiply the top and the bottom by three, you could have 20 over 24, et cetera. So remember, equivalent means that they will represent the same amount of the pi, or that they're equal. So we need to figure out, what does x have to be? So the fraction on the left is equal or equivalent to the fraction on the right, solving proportions. So whenever you see a problem with two fractions and an equal sign between it, to solve something like this, you'll start by cross multiplication. Always remember, two fractions with an equal sign between, you're going to cross multiply. So start by making your x, and that will help you pair things up correctly. The five needs to multiply with the 3x plus six, and the six gets to multiply with the 3x minus one. So now when we solve this, we will do the distributive property twice, once on the left side, once on the right. So five times 3x is 15x. Five times a positive six is plus 30. Then on the right hand side, six times 3x is 18x, and six times a negative one is a negative six. Now it's just an algebra problem to solve. I'm going to subtract a 15x from both sides. So I have 30 equals 3x minus six. And then it looks like I need to add six to both sides. So I get 36 equals 3x. When I divide both sides by three, I get x to be 12. So my answer to this problem is x equals 12. And what that's telling me is that if I replace the x with the 12, well, let's see what happens. Three times 12 is 36 minus one gives me a numerator of 35. And on the bottom, 3 times 12 is 36 plus 6 gives me 42. So that's saying that 5 over 6 is equivalent to 35 over 42. And sure enough, it is, because if I do 5 times 7, I get to 35. And 6 times 7, I get to 42. So x equals 12 is my final answer. And it's what I needed to make those two fractions equivalent.