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Video: Solving One-Variable Equations Involving Negative Numbers

Tim Burnham

Solve the equation 𝑥 − 27 = 5.


Video Transcript

In this question, we’ve got to use mental methods to solve the equation 𝑥 minus twenty-seven equals five.

And we could solve this using inverse operations, and just balance the equation algebraically on paper. So that would mean writing 𝑥 minus twenty-seven equals five. And then using the inverse operation of taking away twenty-seven, so that’s adding twenty-seven, in order to eliminate for that from the left-hand side. But if we did that to the left-hand side, I’m gonna have to add twenty-seven to the right-hand side, to get those t- two things to balance up.

Now looking at this, on the left-hand side here we’ve got 𝑥 minus twenty-seven and then I’ve got to add twenty-seven. So if I add twenty-seven and take away twenty-seven, I’m just gonna end up back with 𝑥. So on the left-hand side, I’ve just got 𝑥, and on the right-hand side, I’ve got five plus twenty-seven. Well that’s equal to thirty-two.

Well that’s all well and good, but we were actually asked to solve this using mental methods, not written methods. So let’s interpret the equation. 𝑥 minus twenty-seven equals five, means something take away twenty-seven equals five. So I need to think, what number is five greater than twenty-seven, so that when I take away twenty-seven from it, I get left with five? Well I can picture the number line in my head, and the number that’s five bigger than twenty-seven is thirty-two.

So no matter which method I use, I get the answer thirty-two.