In this question, we’ve got to use mental methods to solve the equation 𝑥 plus 28 is equal to 10. Now we could solve this using inverse operations and just balance the equation. Now the inverse of adding 28 is subtracting 28, so if I subtract 28 from both sides of that equation and then when I look at that on the left-hand side here, I’ve got 28 take away 28. Well those two things cancel out, so I’m just left with 𝑥.
And then over on the right-hand side of the equation, I’ve got 10 take away 28; well that’s equal to negative 18. Now our full written algebraic working out would have looked like that, and this is all well and good, but we were asked to solve this using mental methods, not written methods. So while that’s correct, we haven’t actually answered the question.
Now 𝑥 plus 28 equals 10 means something add 28 equals 10, so I’ve gotta think what number is 28 less than 10. Now if I can visualize a number line and I’m starting at 10 and I’ve gotta go 28 to the left of that in the negative direction. Well if I take 10 steps back from 10, I end up at zero. So I’ve taken 10 of my 28 steps to the left. That leaves me with another 18 steps to the left. So I’ve gotta go negative 18, so this number is 18 to the left of zero. So our answer is negative 18.
So visualizing the number line is a mental method that helps us answer questions like 𝑥 plus 28 equals 10. You have to think what that means — in this case something add 28 equals 10 — and then translate that into a thought like this — what number is 28 less than 10? Then by splitting up your journey on the number line, you can soon get to the right answer.