Video: AQA GCSE Mathematics Foundation Tier Pack 3 • Paper 1 • Question 3

Solve 𝑥 − 12 = 48. Circle your answer. [A] 𝑥 = 36 [B] 𝑥 = 4 [C] 𝑥 = 60 [D] 𝑥 = 70

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Video Transcript

Solve 𝑥 minus 12 equals 48. Circle your answer. Your options are 𝑥 equals 36, 𝑥 equals four, 𝑥 equals 60, or 𝑥 equals 70.

So we got our equation, which is 𝑥 minus 12 equals 48. So what I’m gonna do is solve it the traditional way. Also, I can show you how we could reach the final answer with elimination. So if we got 𝑥 minus 12 equals 48, so what we want to do now is apply the inverse operation two minus 12. And that’s because we want the 𝑥 on its own because we want to work out what 𝑥 is. So therefore, to cancel out the minus 12, we’re gonna add 12. And that’s because negative 12 add 12 is zero.

So on the left-hand side of the equation, we’re left with 𝑥. And then, whatever we do to one side of the equation, we must do to the other side of the equation to keep it balanced. So we’re gonna add 12 to the other side of the equation as well. So when we add 12 to 48, we get 60. We can work this out using some mental arithmetic by adding two to get to 50 and adding 10 to get to 60. But also, we could have used the column addition method. So we’d have eight add two which is 10. So we put a zero in the units column and carry the one into the tens column. Then, we have four add one which is five add the one we carried, which gives us the 60 that we calculated using our mental method. So therefore, we can say that the solution to 𝑥 minus 12 equals 48 is 𝑥 equals 60, which is the third answer. So I’ve circled that.

Okay, I also said that we could have used reasoning to get to the final answer. So if we take a look at the question, we have 𝑥 minus 12 equals 48. Therefore, the number that 𝑥 is take away 12 gives us 48. Well, 12 is positive. So it’s a number take away a positive number gives us 48. So therefore, we know that 𝑥 must be greater than 48. Because if it was less than 48 and you took 12 away from it, then it would not give you 48. So therefore, we can rule out 𝑥 equals 36 and 𝑥 equals four because these are both less than 48.

And then, we can do 70 minus 48 just to check that 60 is correct. And if you do 70 minus 48 using the column method, we’d have zero minus eight which we couldn’t do. So we borrowed a 10 from the tens column. So we’d have 10 minus eight is two. Then, we’d have six minus four which is two which will give us 22, which isn’t 12. So therefore, the correct answer is definitely 𝑥 equals 60.

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