Solve Two-Step Equations
To solve equations, we do the opposite of what’s currently happening to our variable. So for example, 𝑥 add three equals seven. We are adding three to our variable. So the opposite of add three is subtract three; so we would subtract three from both sides because whatever you do to one side, you have to do to the other. And then when we subtract three from both sides, this just gives us 𝑥 on the left-hand side. And on the right-hand side, we have seven minus three which is equal to four. So we would have 𝑥 is equal to four. Now this is a one-step equation because quite simply we’ve done one step to solve for 𝑥.
Let’s have a look as the title of the video says “two-step equations.” So quite simply we’ll have to do two steps to solve for 𝑥. So solve two 𝑥 plus six equals eight. Now what we want to do as we said is get everything away from the 𝑥. So currently what’s happening to the 𝑥 is it’s being timesed by two and then we’re adding six. So we always wanna get the thing that’s happening to it last off it first. So in this case, we can see that the thing that’s happening to it last is add six. So the opposite of add six is subtract six; so we’re going to subtract six from both sides and this will give us two 𝑥 on the left-hand side is equal to six minus eight which is two.
So now we’re saying two multiplied by 𝑥 equals two. Well, the opposite of multiply by is divide by. So we need to divide both sides by two. Remember whatever you do to one side, you have to do to the other. So dividing both sides by two, this will give us 𝑥 on the left-hand side is equal to two divided by two which is one. So going right back to the beginning, the way that we knew which step to do first, because we could have divided by two first but then we would have had to divide every single term by two and that gets a little bit more complicated. So what we do is we look for the last thing that’s happened to the 𝑥. So we know the last thing is an add six. So we need to get rid of that first and then we’re just left with two 𝑥 equals two.
Let’s have a look at a different one. So we got 𝑥 add three all divided by two is equal to six. Now we want to look for the last thing that’s happening to the 𝑥. So in this case, what’s happening is we’re saying 𝑥 add three and then we are dividing by two. So the last thing that’s happened to the 𝑥 is the dividing by two. So in that case, we’re going to have to get rid of that first. Well, the opposite of divide by is times by. So we’ve to times both sides by two because whatever you do to one side, you have to do to the other. And in timesing the left side by two, it’s getting rid of that divide by two. So we’ve just got 𝑥 add three and that’s equal to six multiplied by two which is twelve.
Now we’ve got 𝑥 add three equals twelve. For the opposite of add three is subtract three. So whatever we do to one side, we have to do to the other; so we’re going to have to subtract three from both sides. And that will give us- well on the left-hand side, we’ll just have 𝑥. And on the right-hand side, we’ll have twelve minus three which is nine. So 𝑥 equals nine is our final answer. You can of course check any of these by putting them back into the original equation and seeing if the left-hand side is equal to the right-hand side. So in this case, we would say nine add three all divided by two equals six. Well nine add three is twelve and twelve divided by two is six. So we know we have it right.
So our things to remember when we’re doing two- or even more-step equations is first of all look for the last thing that’s happening to the variable. Obviously, the thing is an operation; so add, subtract, multiply, divide to the power of whatever. So we’re looking for the last thing on the variable. The next thing we wanna do is get rid of that; so we’re then going to do the opposite. And then we essentially do those two steps the whole way until we just get to our variable is equal to some number. The other thing to remember is whatever we do to one side, we have to do to the other. And there we have it. So if we follow those rules every single time, we will be able to easily solve any equation given to us.