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GCSE maths question HELP

I've been doing paper 1 of the specimen papers for the AQA 9-1 maths GCSE and I'm so confused about question 25 because the mark scheme is very short and so I don't understand the steps that have happened in-between.
I've attached screenshots of both the question and the answer from the mark scheme

so far I understand where the 2cx + 10 + c comes from
but I thought you should do 2cx + 10 + c = 6x + d but then I don't know where the d would go because the mark scheme suddenly has 2cx = 6x :/

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Reply 1

Kevin De Bruyne

Original post by awkwrdbby

The mark sucks because it doesn't use words, it should say 'by comparing coefficients of x'

It's like saying 2=2, if ax+b = cx+d then a = c and b = d. To see this, take x=2, you have 2a + b = 2c + d.

Take x = 3, we have 3a + b = 3c +d.

Now substitute one into the other (substitute 2a + b) to give 3a + b = (2a + b) + a = 3c + d = (2c + d) + a = 3c + d, hence a =c and so b = d.