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.
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@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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