The Maths Prof Solving Linear Equations part 1

hey guys in this video I'm going to show you how to solve linear equations so when say solve equations just mean working out the value of the unknown letter so in the first one we're going to be working out so to work out the value of the unknown vector well you might get to get on the first one and just work out to get work what this number is but that message won't help you long time so we need message that's going to work for every solving equation question so what we need to do is undo everything that surrounded until is by itself so in order to do that we need to do opposites so as the opposite of Adaline is subtracting the opposite of multiplying is dividing and opposite of squaring it square rooting and so on so here need to do the opposite of adding 4 so I'm going to subtract 4 but can't just subtract 4 the next time so have to do the same on the right hand side of equals to keep the equation balanced so on the left hand side 4 take away 4 without just 0 so you'll find whenever you do off of it it always cancels and so on the right hand side you have to calculate so 22 take away 4 without 18 so I've got that 3x left over here on the right hand side and now has 18 it is currently being multiplied by 3 so remember the opposite of multiply is divided so need to divide by 3 and remember to do the same thing on both sides of the equation so where we do the opposite that cancel because 3/3 is 1/5 is 1x and on the right hand side 18 divided by 3 is 6 so we've solved our first equation just something want to point out because some people try and divide by 3/3 always leave whatever is closest to the letter until the end so work your way from the outside in so get this number before this one okay now on to number two so here's our unknown we have to work out the value of so need to get rid of the minus three so the opposite of minus is plus somos it actually and remember to do se on the left hand side of equals as well on the right hand side cancels because that's where we're doing the opposite that just goes to zero and on the left hand side 13 plus 3 is 15 and over here I've still got my form now why has been multiplied by 4 remember the opposite of multiply is defined so need to divide by 4 remember in sitting the same on the left hand side of the equals as well so here's where do the opposite 4 divided by 4 is 1 so that's gone and unless is and on the left hand side 16 divided by 4 is 4 so there we go now onto this bottom one need to get rid of this side although it's little bit confusing because of the model here but we need to look at the sign of that 5 and it's positive side although know you don't like that plus sign you need to remember that because if is positive 5 so the opposite of positive 5 is negative so we're subtracting 5 on both sides of the equation so here they go to 0 sine is negative 2x and on the right hand side 65 degree negative 5 or just take away 5 is negative 10 and then do the opposite here what is being multiplied by negative 2 so the reverb is to imply by negative 2 so remember it canceled out where we do the opposite and on the right hand side negative 10 divided by negative 2 is positive 5 okay so I'm going to change them up bit and make them look bit different okay so in these next two examples I'm going to continue doing the same thing and I'm going to undo everything that's happening around unknown until found the value of letter so in this one need to get rid of this big fraction remember when we see this line this means divided by two and the opposite of surviving is multiplying so in this one I'm going to multiply both sides of the equation by two so remember we're going to do the opposite it cancels so you're just left with 3x plus 1 and on the right hand side you have to calculate so 10 2 is 20 and now it's just looking like one of those questions did earlier so have to subtract 1 on both sides of the equation here in cancels and I'm left with 3x on the right hand side 20 take you okay take away 1 is 19 and then need to divide both sides by 3 so there it cancels and so this one can't divide 19 by 3 so I'm just going to leave that as fraction or maybe you'll be asked to write your final answer as mixed number in which case you will need to say how many threes fit into 19 6 what's left over 1 and then the denominator stays the same but if it doesn't ask for mixed number then you can just leave it like this because this is simplified fraction we can't simplify it so in actual fact it was very similar to the questions from before it was just the first step in order to get rid of that the exceptions you have to multiply it by 2 now in number 5 is little bit different because we have fraction and lumber well there's more than one way of doing this question lots of people 4 and they multiply by 4 here but they forget to multiply by 4 here so would probably start by adding 2 on this one instead so when go there before always leave whatever is closest to the nectar until the end so lose these pop link+ together and get rid of this step so here I'm doing the opposite and so I'm going to cross that out and I'll is over 4 on the right hand side need to calculate it so that gives me negative 6 and now the opposite of dividing by 4 is 2 4 remember this is always the same thing on both sides of the equation can't when you do the opposite it just cancel so I'm left with and on the right hand side unless calculate this so negative 6 times 4 is negative 24 okay so I've got one more challenge questions to finish okay so in this last example we've now got brackets to be always so remember when using bracket means multiply so here with more time the bracket 3 is 3 so you could think okay I'm going to divide both sides of this equation by 3 so that would come from here but when look over here this number isn't divisible by 3 so I'm going to get that idea and I'm going to multiply out the bracket so let's do that so 3 multiplied by is 3x and we multiply by negative 7 is negative 21 and 25 hasn't moved so now it's just like they start forwards from the beginning of the video and need to undo everything around so the opposite of subtracting 21 its absentee one remember to be the same thing to both sides the left hand side cancel because we get 0 here and on the right hand side if add those together again 46 so the time of step at the moment is being multiplied by 3 have to do the opposite and decide wisely so suffice both sides of the when three on the left hand side the left one it and on the right hand side I'm next with 46 over three and can't simplify that fraction so I'm just going to leave it like that so there's my first video and solving the linear equations will have another one coming up soon where you've got unknown for both sides of the equal signs to look out for that one and so that's it for today