Can't figure out why sign flips form plus to minus in algebra equation. Equation goes like this:

Question

6=267a - 47b. We have figured out that b = (12 + 47a)/147. So we substitute:

6=267a - 47((12 + 47a)/147). We figure we can multiply both inside numbers by 47 and divide them by 147. Becomes

6=267a - (47x12 + 47x47 x a)/147 followed by

6=267a - (564/147) + (2209a /147) example continues

6=267a - 3.8 - 15a

 

I cannot figure out why the two number that were previously added are now subtracted.

Thanks Neal!

Answer 1

6= 267a - 47b

b= (12+ 47a)/147

substitute

6 = 267a -47(12+47a)/147

multiply by 147

6(147) = 267(147)a - 564 - 2209a

(2209-39249)a = -564 -882 =-1446

a = -1446/-37040 = about 0.039 or 0.04

you have 252a = 9.8 rounding off to 1 decimal

a = 9.8/252 = about 0.039 or 0.04

you did it all right

you added two numbers inside the parentheses, then they became negative, subtractions, due to the negative sign in front of the parentheses.

-(a+b) = -a-b. you added them, but now subtract them