Video: Solving Two-Step Linear Equations in a Real-World Context

Jacob’s destination is 90 miles away. He drove 80 miles already. Solve 90 − 𝑚 = 80, where 𝑚 represents the number of miles which he has yet to drive, to determine 𝑚.

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Video Transcript

Jacob’s destination is 90 miles away. He drove 80 miles already. Solve 90 minus 𝑚 equals 80, where 𝑚 represents the number of miles which he has yet to drive, to determine 𝑚.

So if we take a look at this equation, 90 minus 𝑚 is equal to 80, there’re a couple of ways in which we can solve it. The first way, and probably the easiest way, is to think about it mentally and think what 90 take away what is gonna be equal to 80. And similarly, 80 add what will give us 90.

Well, if we think about it, 90 take away 10 would give us 80. And 80 plus 10 would give us 90. So therefore, 𝑚 is equal to 10. I found that using the mental method. And we could double check it because if you think 90 take away 10, well think about nine take away one, that would just be eight, which is our 80, which what we wanted. And similarly, 80 plus 10, well let’s think about eight plus one which is nine, add the zero on, 90, so that would work.

However, I did say there’s a more formal method. And the more formal method would be to solve the equation using inverse operations. So the first operation we’ll complete is to add 𝑚 to each side of the equation. And the reason I’d add 𝑚 to each side of the equation is because we don’t want to have a negative 𝑚. It’s easiest to do with when it’s positive. So now, we’d have 90 is equal to 80 add 𝑚.

Well, the next stage to help us to find out 𝑚 is to subtract 80. And that’s because we want 𝑚 to be on its own. And whatever we do to one side of the equation, we must do to the other side. So if we subtract 80 from each side of the equation, we’re gonna get 𝑚 left on the right-hand side of the equation. And on the left-hand side of the equation, we have 10. And that’s because 90 minus 80 is 10. So now just to show how you’d work that out using a written method because we used a mental method previously, you got 90 minus 80.

First of all, we have zero minus zero, which is just zero. And then, you get nine minus eight, which is one, to get an answer of 10. So therefore, we can say that we fully checked our answer. And we can say that if Jacob’s destination is 90 miles away and he drove 80 miles already, 𝑚, which is the number of miles which he has yet to drive, is going to be equal to 10.

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