SM2 17.2.3 Solving for Multiple x’s in a Fraction

Added: 2026-04-29

[00:00:01]Hello and welcome. So we're going to be solving  our equation here for x. Now your goal is x equals and right now we have more than one x.  Now you might be looking at this and you're like oh we have an x over x so surely I could  just take those x's and cross them out. No you most certainly cannot cross those out and the  reason why is because of those addition symbols, right? It's kind of like if you have like 2 plus  7 divided by 2, right? It does not equal 7. That's not a true statement. You can't just cross out  the twos because of addition. If you were to do that separately, right? You would do 2 + 7 which  is 9 over 2. Nine halves is wildly different from 7 if you were to try to cross those out. Okay.  So whenever you have addition you cannot cross stuff out top and bottom with a fraction. All  right. So if you can't cross anything out your only option is to undo the fraction. Well think  about it fractions are the operation of division.

[00:01:04]How do you undo division? Multiplication. So  multiply by (4x + 9) on both sides because what you do to one side you do to the other. All  right. So denominator and what you multiply by will cross out because you undid the division.  It was technically over one that's why it goes the way of the dinosaur there. Okay. And then you have now y times (4x  + 9). Okay it is parentheses because you were multiplying by 4x plus 9. You're multiplying by  that whole thing so you need to use parentheses to keep it together. And then equals 5x + 8. All  right. Now your goal is x equals. Remember your goal meaning that you want all of your x's on the  same side. You want them together. So that means that the parentheses with the y in front not doing  you any favors. Get rid of it. Distribute the y through so 4xy + 9y. All right. Now remember your  goal all of the x's have to be together for your goal to happen. So that means we need to move  them together. Pick a side to have everything on. It's either we can move the 5x to the left  or you can move the 4xy to the right. Whichever way you go it doesn't matter. I like having my  x's on the left so I'm just going to move my 5x.

[00:02:31]Okay. And when I do that um I'd say okay  so we have 4xy minus 5x plus 9y equals 8.

[00:02:42]These two terms cannot combine and the  reason why is literally the y. It's the letter y is what's stopping you there. Because  they're not like terms they can't combine. So you still want everything with an x on  the same side. Does your 9y have an x?

[00:03:00]No. So let's move that over. It's not going to  be helpful for us. So 4xy - 5x equals 8 - 9y.

[00:03:12]Now final step here this is kind of the one that's  hard to see. Is you say okay, I have two terms. Term number one has an x. Term number two has an x.  What do they have in common? An x. Pull it out.

[00:03:28]What we're going to do is we're going to take the  idea of a greatest common factor GCF. We're going to use it to pull the x out. So if I pull the x  out of 4xy, 4y remains. If I pull the x out of negative 5x, negative 5 remains. And now you'll notice that in your  equation you only have one x there. Now keep in mind we said GCF. If your numbers had something in  common you actually wouldn't pull it out and the reason why is because you want an x and you want  x equals. Meaning if you put anything else next to it you're just going to have to move it over  in another step. So even if those had a number in common don't take that out. You want just the  common factor of x not the greatest common factor.

[00:04:16]Okay. All right. So last step you want x equals.  That is your goal, right? So now you'd say great what is attached to my x? The parentheses. We need  to move the parentheses. What operation joins the x and the parentheses? Multiplication. You undo  multiplication with division and it's a valid move to divide by that entire parentheses and these  will cross out. And the reason why is because that is multiplication. If that was addition or  subtraction you couldn't. Keep that in mind you would use a different operation to move it. All  right. So from there you have a fancy one. Those cross out. It leaves you with just the x. That's  your goal. On the right side we now have (8 - 9y) over (4y - 5). Can that simplify in any way shape  or form? No because you have subtraction there, right? Unless all four numbers had something  in common you couldn't simplify it. All right.

[00:05:18]Now your goal was x equals. Do you have x equals?  Yes. You are done. It's okay that it's a fraction on the other side. That's totally fine. It could  look like something gorgeous or something nasty.

[00:05:31]Whatever your goal was which was x equals you  accomplished. You're done. Call it a day. All right. So we have solved for x and those are  your steps. Thank you so much for watching.