﻿Hi everyone, Ms Jones here. Today we're going to be looking at reviewing solving equations. Now that's hopefully a topic that you have done before and you can remember how to solve those equations, but if not, please do refresh your memory and ensure that you are really familiar with this topic in detail before we can begin 'cause today is mostly just a recap on that topic. Before we can begin however, please make sure you have a pen and some paper and that you have removed all the distractions from around you and you can try and find a nice quiet space to work. So pause the video now to make sure you've got all of that ready so we can begin. Okay let's begin. What number could Zaki be thinking of? He's saying, "If I subtract double my number from 15, "I get the same as when I add five to triple my number "then divide by two." So you can use any method you want to try and figure this out, you might want to use trial and error, you might want to use something a little bit different, but it's just about having a go. So pause the video to have a try at this. So if you used trial and error, you might've done a few different numbers but you may have noticed that if you put in, for example, three, we get quite close to being the same, but not close enough, and with four, again we're quite close, so these are the closest we're going to get to having the same, but neither of them are exactly the same. So actually our number is somewhere in between three and four, so we can see that I've substituted three in here because I'm subtracting two lots of three from 15 and we're trying to find out if it's the same as when I add five to triple my number, so I've multiplied by three and added five and then it's being divided by two. So we're going to see now why it's really important to have a bit of a more formal method of working this out because actually sometimes it's not possible to just have a go and try with different numbers or you have to be trying a lot of different numbers so you can really get the exact answer here. So this is where forming and solving equations really gets its value. So we're going to try and set up an equation first of all, now remember when we say that we don't know something, if we're looking for a number that we don't know, we can call it a letter and quite often that letter is X, but you can use other letters if you want to, but I've used X for this one. So I'm subtracting double my number from 15, so I know I'm subtracting two lots of some number, two lots of X, which is where this has come from, from 15, so that's the first side of my equation. Because it says I get the same as, the same as is the same as equal to as when I add five, so adding five to triple my number, three lots of my number and then divide by two. So it's really important that you break that down because there's quite a lot of information there and there's quite a lot to set up in your equation. Now in order to solve this equation, I'm trying to find my missing number, I'm trying to find X and we've got a lot of Xs going on here, so quite often, and you've seen it before when you were learning this topic before hopefully, that we can draw a bar model to help us, so I've set up a bar model here, I've done my 15 subtract two X, which is this part here is the same as half of three X add five, so that's half of that section there. This is still going to be quite difficult to solve at this point, so we need to balance that equation. So what I'm going to do is I'm going to try and get rid of that divide by two 'cause that's making this quite tricky because I don't know what half of this section is. But in order to get rid of divide by two, I need to multiply it by two, that removes that and we multiply this side by two and we end up with this, 30 subtract four X is the same as three X add five. So now I've got 30 subtract four X, so I've got this section is the same as three X add five. My next step is trying to get the Xs on one side because, again, I need to find that X and I can't find it when I've got it on two sides, it's quite confusing. So I want to put my smallest value of X, smallest coefficient of X which is the subtract four, negative four, and I'm going to put it on the other side. So I'm going to move these four blocks to the other side, add four X here and add four X here, get rid of this bit, so I've now got 30 is the same as seven X add five and that looks much more simple and we're getting there, very close now. So what I want to do next, again, I'm just trying to find what one of these Xs is, so I'm going to get rid of this five from both sides, just subtract it from both sides. We end up with 25 is seven X and once I've got that, I'm just trying to split 25 into seven equal parts, which is a fraction, 25/7 and I've made that into a mixed number just to make it clear that actually the answer was in between three and four and it would've been quite tricky to just try and guess that answer, it would've been something that you'd be unlikely to guess so we needed to solve that equation and this is one method that we could've used. Using the bar model helps us to visualise it, although it can get a little bit tricky when we've got those longer, more complicated equations, but hopefully, the whole point of this is finding X and you can work through the steps to do that. If you want a little bit of extra support on this because you've forgotten a little bit about this, then again, go back to those year eight lessons if you need to. Pause the video now to complete your independent task. So your independent task, the first question was a few of the examples, similar to what we've done in the connect task. The second part was looking at perimeter, but actually it's very, very similar, you're just setting up an equation and solving it. So these are the answers that we should have got. I won't go through another one of these ones because we did them before, but I'll go through question two. So the triangle and the rectangle both have the same perimeter, find X. So the first thing, if I'm looking at perimeter, I know I just need to fill in those other sides to make sure I've definitely included everything in my perimeter, because remember the perimeter is the distance around the outside of the shape, then I'm going to set up my equation. This perimeter of the rectangle is going to be two X add six, and this perimeter is going to be, X add X add X is three X add four. And it's telling me these perimeters are the same and remember the same, we can write as equal. Then I need to solve my equation, so I can remove this two X first of all from both sides and I'm left with six equals three X add four and then again to find that X on its own, going to remove the four from this side and whatever I do to one side I do to the other, so I'm left with three X, oh sorry, it's one X isn't it? We've removed the X. X equals two is what I'm left with. And that's my answer there. For this one, it was a little bit of a trick because instead of finding X, which is what we all like to do, we like to find X and we like to stop, it's actually asking you to find the perimeter, so you had to substitute X back into those that perimeter, that expression of that perimeter. Really well done if you managed to get those, there were quite a lot of complicated questions in there, but actually, once you've set up the equation, it shouldn't be too difficult to solve it, so really, really well done if you managed to do that. Now for the explore task. By placing the cards in the equation frame which is this here, and solving it, different values of X are found. So we've got four different expressions here, three X, two X add four, five X subtract three and six subtract X. Which combination of cards give the greatest value for X, the least value for X, and the same value for X? So you're going to have to do a little bit of experimenting and a lot of practise of solving equations by putting in these expressions into this equation. Pause the video to have a go at that. So really well done if you managed to get any of these answers. The greatest value for X was actually four and that happens when three X equals two X add four. And hopefully you can see straight away that we subtract two X from both sides, we end up with X equals four. The least value for X was 2/3 and this occurs when six subtract X equals two X add four. And finally, the same value for X, a few of the equations had the same value for X and that value was 1.5 and that happens when three X equals five X subtract three, five X subtract three equals six subtract X, or three X equals six subtract X. Amazing job if you managed to get all of those and even if you managed to get some of them, really, really well done. That brings us to the end of today's lesson, so massive well done and thank you for sticking with reviewing solving equations, you've done really, really well today.

What is the purpose of solving an equation?

Which of the following can be values when solving equations?

What is the value of x for x - 4 = 3x + 2?

What number am I thinking of, if half of the sum of my number and 4 is the same as 3 lots of my number subtracted by 2?

The perimeters of the rectangle and triangle are the sane. What is their perimeter?

Reviewing Solving Equations Quiz

In this lesson, we will review how to solve equations. We will then convert worded operations into algebraic terms to make them easier to solve.

Maths

Y9 Maths

Key Stage 3

Year 9

Miss

Reviewing solving equations

Solving linear simultaneous equations algebraically

Algebra

THEME

UNIT

Equivalent equations

Linear relationships

Combining algebraic relationships

Exploring expressions with two variables

Exploring systems of equations

Solving simultaneous equations

Writing simultaneous equations algebraically

Checking the solution of simultaneous equations

Solving a simultaneous equation algebraically

Eliminating a variable

Manipulating systems of equations

Solving word problems

Using substitution to solve simultaneous equations

Substitution or Elimination

Simultaneous equations by trial and error

Let p be the number of protractors bought. If each protractor costs £2, which of the following represents the total amount spent on protractors (in pounds)?

If x=2 and y=3, what is the value of 2x+3y?

Use substitution to decide which of the following is the solution to x+y=3 and 5y+3x=15.

Fill in the gaps: The "n" in the nth term represents the ____.

Which sequence is formed as a result of adding "4, 9, 14, 19, ..." and "12, 8, 4, 0, ..." together?

I want to buy 3 rulers and 3 protractors. If they cost 40 pence each, how much will I spend?

If p+1=6 and p+q+1=7, what is the value of q?

4x +8y=116 AND 4x +4y=68. Solve

Is there a solution with x value between 0 and 1?

Look at the picture below and then fill in the gap: If two equal expressions are both __________ by the same quantity, then the two resulting expressions will be equal.

3x+2y=5 AND 3x-2y=7.  If I add these two equations together, which unknown will be eliminated?

Lesson overview:Reviewing solving equations

Core Content

Solving linear simultaneous equations algebraically: