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Let $p(x) = 2x - 7$ and $q(x) = 3x - b$. If $p(q(4)) = 7$, what is $b$?

 

Thanks! Please include the steps I don't just want answer I want explanation as well so that I can do problems like this by myself soon. 

 Apr 28, 2023
 #1
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We have that p(q(4))=7. Substituting in the definitions of p and q, we get:

p(q(4)) = 2(3(4) - b) - 7

12 - 2b - 7 = 7

-2b = -8

b = 4

 Apr 28, 2023
 #2
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sorry but that is wrong

 Apr 28, 2023
 #3
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q(4) = 3*4 - b  or  q(4) = 12 - b

 

p(q(4)) = 2*q(4) - 7   or  p(q(4)) = 2*(12-b) - 7  or  p(q(4)) = 24 - 2b - 7   or  p(q(4)) = 17 - 2b

 

But p(q(4)) = 7, so  17 - 2b = 7   or 17 - 7 = 2b    or  10 = 2b   or  b = 5

 Apr 29, 2023

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