Set up AND EVALUATE an integral that computes the (lateral) surface area of the solid generated by revolving the curve:

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal

-3(b-8)-5=9(b+2)+1

distribute

-3b+24-5=9b+18+1

add/ subtract

-3b+20=9b+19

20-19= 1

-3b+1=9b

9b+3b= 12b

1=12b

1 divided by 12 = 1/12

answer: 1/12 = b

the answer is b 4pi/3

got it down chief.