19/4x+1 = 9x+1/5x-1

Question

19/4x+1 = 9x+1/5x-1

 

x=?

 

a) 41
b) 17
c) 13
d) 2
e) –5

Answer 1

Use cross multiplication:

 

19(5x-1) = (4x+1)(9x+1)

 

95x - 19 = 36x² + 13x + 1

 

36x² - 82x + 20 = 0

 

18x² - 41x + 10 = 0  solve with the quadratic formula

 

[41 +/- √(41² - 4(18)(10))]/(2(18)

 

(41 +/- 31)/36 = 10/36 or 72/36 = 5/18 or 2  answer d

Answer 2

On this platform, where a ratio has to be put in as a single line, IT IS NECESSARY TO ENCLOSE DENOMINATAORS AND NUMERATORS IN PARENTHESES whenever they are the least bit complicated (such as having two or more terms).

 

Fix that. Then you have a proportion; cross-multiply, then collect like terms and solve. Check your work.