# Algebra problem: Can you help?

Afternoon, I’m just doing a bit of algebra revision on the BBC GCSE Bitesize website and one question has stumped me: I can’t figure out where I’m going wrong.

Here is the question:

4. If a = b – c, then:

a. c = b – a

b. c = a + b

c. c = a – b

Apparently a is the right answer, but I can’t work out how to get there.

I’ve been taught that when letters/numbers change sides they change their sign as well, therefore I answered b.

Any help is appeciated :) (I could just ask my Maths teacher on Monday but I’m rather impatient)

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## 8 Answers

Yes, but “a” changed sides as well; therefore it would be negative in the answer…

Yes, as above. -c =a – b therefore +c= -a +b

Add C to both sides and subtract A from both sides, voila !

Keep in mind that you can do whatever you want to one side of the equation as long as you do the exact same operation to the other side.

Welcome to Fluther.

@dabbler has given you the correct answer and the methodology.

Ah right I see where I was going wrong now. Thank you.

The above answers are correct. I’ll now show it in even more detail.

a = b – c

a + c = b – c + c

a + c = b

a + c – a = b – a

c = b – a

You can always substitute numbers to check your answer.

if a = 7, b = 10 and c = 3 then the answers says 3 = 10 – 7

On a multiple choice test, you can use this approach to get the answer by process of elimination, but I would not recommend doing that.

*I’ve been taught that when letters/numbers change sides they change their sign as well…* Not a very reliable rule, as you’ve already seen. A better rule, which you can always count on, is that you must perform the same operation on both sides of the equals sign – as mentioned by @dabbler.

In this problem, a = b – c, you can add c to both sides, then subtract a from both sides, to arrive at the result c = b – a.

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