Question

a(x+7) + b(x+5) = x+1

Find a - b

Answer 1

\[\Huge x(a+b) + 7a + 5b = x+1\]Now what?

Answer 2

the constants are equal; the coefficients of x are equal, that is \[\huge 7a+7b=1\] \[\huge a+b=1\]

Answer 3

correction: the first equation is \[\huge 7a+5b=1\]

Answer 4

And a+b = 1 too?

Answer 5

yes, that's right.

Answer 6

So a - b = -5?

Answer 7

yup.

Answer 8

Well, that was easier than I excepted, but what if I have something like this:

x(a+b)+7a+5b= -1(x+1)

Answer 9

-(a+b) = 1

-(7a + 5b) = 1

Right?

Answer 10

@sirm3d

Answer 11

right. just compare coefficients of x and constants.