well there we have got another algebraic equation uh concept that we need to focus with work out our equations as a typical exam question on question number three so let's see what we are given question 3.1 solve for x so this is what we are given on the first part uh 3.11 uh that is to solve for X7 - 3x is = to 2x- 3 and that is three marks for that so depending with the way that you are going to solve but I say that whenever you are given this condition where you have got the terms of X separated another part of X on its own and also considering the constants we can collect the like terms when it is like that considering the terms of x to one side of the equation so collect like terms so we are going to collect like terms in that case meaning to say the terms of x to the one side knowing that once the term or a number crosses the equal sign or jumps the equal sign it changes the side so that will be Min - 3x - 2x it was a positive on this side A minus let's take out uh this other part the seven we can take it to the other side of the equation it was a positive 7 so this side will be a minus 7 so that is minus 3 Min - a 7 all right - 3x - 2x these are like terms and therefore you're going to obtain - 5x which is equal to - 3 - 7 which is a -10 from our multiplicative inverse the multiplication simply divide by the number that is Multiplied so we are simply going to divide by A5 so X was going to give us a positive two 10/ 5 that is a two so you can also consider that way so do revise as many questions so that you do understand uh these Basics all right 3.12 again we given uh that is 10 - 4 into the bracket of 2x - 1 is equal -2 into the bracket of 3 - x if you are given the brackets whatever that given consider the same way that you do work your algebraic expressions remember concept of expansion of the practice before you think of solving the equation solve I mean simplify the same part that you do on your Expressions expanding of brackets collecting of like terms that part can play a role all right so then the minus 4 is the one that is to be distributed to distribute everything here the minus 4 so it's -4 * 2 which is -8x -4 multiplies a negative one that is going to be a positive for negative negative so it multiplies everything this is equal to on the right hand side we also have a bracket and the number just outside of the bracket is the minus two so distribute that into the bracket - 2 * this 3 that is - 6 - 2 it multiplies the minus X that's a positive negative negative that's a positive 2x all right let's just simplify collect like terms there on the left hand side we've got a 10 and a four 10 + 4 that is 14 - 8 x is = - 6 + 2x so I want you to see something just after expanding of the brackets collecting of the like terms this statement that we are seeing this equation I want you to say this from the first question it is exactly the same presentation that we had here in the first look exactly what we had you expanded the brackets but after that are you say back to the normal P that we had of collecting of like terms again where we need to take the terms with X to one side of the equation Conant to the other part of the equation so still to that cont so they just want you to play around just revise more questions just a repetition here so as you can see here we going to consider the numbers on their own uh the variables on their own that is um already on the left hand side there is A- 8X there so transpose the 2x the moment it crosses or jumps the equal sign changes the sign to a minus to a positive so it's going to be a minus this is equal to already the minus 6 is on the right hand side what we are going to transpose is the 14 to the other side of the equation if it was a positive 14 there it is going to be A4 so we are back simplifying like terms - 8 - 2 that is a - 10 so that's - 10 x - 6 -4 from your calculator that's a uh 20 that you are going to obtain so if - 10x isal to-2 that's a product there the multiplication opposite divide by the number that is multiplying divide by A1 divide by A1 so this will cancel and you have got a 10 into a 20 which is a two so that is our X value there remember negative negative cancels so X was going to be a positive two just like that so you see that uh there is a need you also to revise your algebra those algebraic expressions you still need the idea there the simplification expansion of brackets it's not from equations it's from our normal algebraic expressions but they play a role in solving of the equations now all right another equation that was 3.13 we are given 3x - 1 over a 2 isal to a 4 remember I said uh that we can consider just to remove the two here remember the concept of the multiplicative dividing by two means we can remove these two by multiplying by it since we are dividing we can multiply by two the opposite of dividing multiply remember if it is 2x you divide by two there you dividing so multiply by but whatever that you do on the left hand side must be done also on the right hand side so you multiply by two also or you can simply cross multiply remember I talked about the cross multiplication also 4 over one you cross multiply like this the one multiplies 3x - 1 as it is it remains as it is the two multiplies the four which is eight so you can also cross multiply or you can consider this concept to remove this multiply by its inverse so this will cancel you remain with 3x - 1 = 4 * 2 which is 8 we are back what are we having minus one which is affecting the part of X so simply add it to the other side or jump this to the other side it changes the sign it was a minus it's going to be a plus or you add a one here you add a one there it's up to you so meaning to say 3x - 1+ 1 that's a z or jump to the other side it becomes a plus 8 + 1 which is 9 multiplication divide by the number that is multiplying which is three so X is equal to what 9id 3 which is a three you can also test this by substituting in place of X and see if you are in the right direction so our X the one that was going to satisfy this equation was supposed to be three all right then we are given in this case a word problem which is like a statement that you are given we are given that PO 5 years older than CYO their ages added up to 25 I talked about this type of a person actually then you asked how old is pop and KY they will need both ages both one for Po and one for for KY so given that pop is 5 years older than than Kyo so let's just say this is Po's age let's just say it's X and kyo's age is why let's just say this is what we have and we are given that Po's age is 5 years old I said you can write it in two ways you can write your Edge po ede to be equal to for it to be the same since it is 5 years older you must add to KY Ed so that is y + a 5 so that they will be equal because right now they are not equal this one is older so to be equals either you're going to add that or you were supposed to subtract A5 on PO ede so that you obtain kyos ede which is why it was up to you okay let's say this is what You' have decided to do you've got something like this because there are two letters they are two edges they different so another one is X another one is y their edges this is the statement their ages in years added up to 25 that is the sum in years the sum the age added up to which if if you take the age of poy and you also take the age of Kyo together you add them you must get a 25 so po age it's X kyo's age it's y we do not know their ages but if we add their ages we must get a 25 so the question is how old is Po and KY what how old by finding X and finding Y we have determined po Ed Y which is kyo's Edge so the question is how can we solve this equation okay this is it we can take this as two different equations that is X which is equal to this remember they are saying guys I want us to to to understand this statement X is equal to y + 5 it means they the same these two they the same so what if I take this x here which is y + 5 I take it into this equation in place of this x here where there is X I substitute this I put this as it is remember your substitution method so you substitute that in place of X so meaning if you substitute that in place of X here it is going to be y + 5 remember x and x is equal to Y so you take as it is y + 5 you put it in place of x but there is a plus y that we already have so plus Y is equal to a 25 why are we doing this so that by the moment you substitute this x which is in terms which is written as y there you are formed an equation as we can see which is in terms of Y only there is y here there is y we no longer have X and Y at the same time because we substituted we did remove like we subtrac we are substituting what is equal to that X but in terms of Y so that's another way remember I explained this in the previous class and I said I'm going to wake out different ways that we need so that's another way that you can work with let's see collecting the like terms the part of Y and Y we can add this is one y + 1 y so 1 + 1 that is 2 y + a 5 is = 25 so we can solve by taking the five to the other side transpose or take that to the other side the moment it jumps the equal sign remember I said it must change the sign it was a positive so it will be a minus or just subtract a five here you also subtract a five on the other side of the equation so you remain with the 2 y = to 25 minus a five 25 minus a five which is what which is a 20 so take note so 2 y isal 20 that's a multiplication divide multiplicative inverse divide by two so Y is equal to what 20/ 2 that's a 10 so remember y represents Kyo Edge that's why so we have got Edge there what about po Edge since we have got a statement we have an equation of your age here X is y + 5 what if we just substitute again just like what we did previously but we substitute now the numerical value of y in place of Y we substitute the exact number representing Y which is what a 10 so you put that 10 here in place of Y so it's 10 plus a five so it's called substitution as you can see it's substitution so X is going to be what 10 + 5 which is 15 so this means we have got the edges of these two that is remember how old is pop so many you say x representing what Po's Edge so meaning to say uh in this case PO is 15 years remember it is X so that is 15 years old and on the other hand we have got y there representing Kyro Edge so meaning to say in terms of Cairo in this case Cairo is 10 years old meaning to say that's the age in terms of what you are given there so that is 10 years old just like that so you can actually solve by substituting these values one into another one into until you get what you are given so this one you take advantage Y is equal it can be written in terms of Y so I don't not know how did you present your equations in the first place but after solving you must obtain these values X being 15 and a y being a 10 or these numbers 15 and 10 on your answer so as you can see that's your typical exam question more to come from M African motives till we meet again