Equations with Pronumerals on Both Sides

This lesson we're going to be looking at equations with pronumerals on both sides So far in equations we've looked at what an equation is and we've defined that as a mathematical statement where the left hand side and the right hand side having an equals sign and equalling each other we've also looked at how to solve equations using some informal methods. So some of those are trial and error backtracking and we started last lesson to look at a formal method of solving equations known as the inverse operations method and that is the method you always used unless you are asked otherwise. So in everything, from now on we're going to be using that method. What we're going to be looking at today is how to solve equations with pronumerals on both sides so the important thing to think about first is what is a pronumeral? uh... and basically we've discussed this a lot and you should know by now that a pronumeral is basically some kind of unknown. So it could be a letter of the alphabet, it could be a Greek letter, it could be basically any unknown what do we mean by equations with pronumerals on both sides? what you see here in question 3a that we're going to do later on it means that both the left hand side and the right hand side of the equation have pronumerals on them which is different to your basic equations. You might just have 3x plus 8 equals six in these ones. You can see in this first example, there's two pronumerals and they're not on on the same side so they're a bit harder to simplify. Not very hard just more involving so let's start off by having a look at a few examples together we're gonna go through about 4 examples and I'm gonna go through with you how to set them out. Now please make sure that you write the correct setting out because otherwise you're going to need to do it again so that is really really important. So let's just have a look at these first two examples and we're going to be using the inverse operations method to solve it. so in this first one we've got 4x + 5 equals 3x plus eleven now when solving these sorts of equations the first step is to always get the pronumerals onto one side always that's pretty much how you start so why don't we do that now? and you don't just want to move them onto one side, you wanna move them onto the side uh... that makes the pronumeral positive so the second step is to ensure that the pronumeral is positive. That's my shorthand for +ve uh... where possible it won't always be possible, but where you can you wanna make the thing uh... with the letter positive so here I need to decide, do I want to take away the 3x from both sides, or do I want to take away 4x from both sides? now I have to tell you at this point, whichever way you do it, if you do the correct steps you'll get the right answer. Even if you have a negative pronumeral. ok you can still work it through. Generally it just means a bit more work however i'm going to minus three x from both sides because I know that if I do 4x minus 3x it's going to give me one x so 4x minus 3x is one x I've got plus 5 left 3x minus 3x well that cancels out to give zero and I'm left with plus 11. so remember what you do to one side you do to the other side. If I wanted to get rid of the 3x here, I had to get rid of the 3x here as well Now I want to get x by itself. Well ask your self the question... what's happening to the x? It's being plussed by 5 so I'm going to minus 5 from both sides 5 minus 5 is zero so I'm left with x and eleven minus five is six ok. Now remember you can't just accept this as your answer you should be substituting it back into the equation to check so you can do that as your check as well ok so if i just quickly check over here sometimes you can do it in your head but it's good to show it so I've got 4 times 6 plus 5 uh... that should be equal to 3 times 6 plus eleven now4 times six is 24 and twenty four and five by is 29 3 times 6 is 18 and 18 plus 11 is 29. So it's correct It's always good to do that check, especially if you have time in a test. In a test you don't check it first, you do all the questions first and then you check. otherwise you might run out of time. ok, let's have a look at question b. I'm gonna show the working out here. So, first step, get the pronumerals onto one side, ensure the pronumeral where possible is positive and the third step is to obviously solve for your pronumeral. Isolate the pronumeral. ok, in this one I've got, 4x minus 8 equals 10 minus 2x Now, I wanna make the x thing positive so if I put minus 4x here that's gonna end me up with minus 6x So I'm gonna get rid of this 2x here, so I'm gonna plus 2x to both sides 4x plus 2x well that's 6x and I've still got the plus 8 and that is equal to 10 minus 2x plus 2x is zero so what I've got at the moment is 6x plus 8 equals 10 and now I need to say well what's happening to the 6x? It's being plussed by 8 I wanna minus by 8 on both sides, so just bringing that up to here I'm gonna have 6x because 8 minus 8 is zero. six x and sorry, I'll write that a bit clearer. I'm going to have 6x is equal to 10 take away 8, that's 2 If I want to get x by itself, ask yourself what's happening to it, well it's being times'd by six, so I'm going to divide by six on both sides 6 divided by 6 is 1 leaving me with one x but we don't write the 1 and 2 divided by 6 well that is one third and that's my answer. And again, you can check it. And the best way to check it is probably just quickly with your calculator but that should be the right answer ok. So make sure you've written down the correct working neatly and it should go under each others, so when you write it down on your sheet, you're gonna write this bit here these directly underneath this ok, so that's important ok, make sure you pause the video and get all that written down, including these notes up here they're very important uh... n why don't we just quickly have a look at two more examples, cause you're gonna need to know how to do lots and lots of these questions by yourself so we'll have a look at these two questions them and that's what we'll have time for this time let's have a look at question c it says to wipe out seventies while mine's ok weekend so i'm going to take wave off my from both sides two y minus one y is just one line when asked about the past seven and wanted to let lives here and i think maybe baghdad to get signing it's belongs to the site saic mona's been prospects and so you get rid of the anti minds by seven falsetto five seven zero said that lani a quilting eighty each day that's my insight and again i can't check that bicep sitting in back into the solution k christian d six sampras twenty-fold equals five and i say well i'm gonna subtract by then about science finance at like five minutes here side an active reminders any side on the side of that seek semana spine and which is one m wrapped up last twenty four case it is going up here at my answer just real and that means that the and but thankfully replies thanked i need to get them by itself at the moment is being prospects many false i need to be invests miners by twenty four on both sides uh... trying but a quick training policy red ample endings but he's monday minus twenty four well it's gonna be meeting city too can again you consent to detain teaching but that's pretty much the basis of that have about ten minutes of samples brought them out and we'll practice in my class and get a lot more cheques in class ask questions like any questions you have and she copied a stunningly again the speech should be directly on the link that i just ran out make sure you have a right and she and k say make sure you write down exactly what you learned his lesson anything you can understand you have to write down a high of a stinking question now we're down to the highly thinking questions are higher but you still can think of the questions ask maybe some uneasiness in class or anything way you'd have to let this sink ok sam and she filled out these two questions for him five as well going to do it she stick it in your book and i've seen examined boxy letter