I really don't understand this so i would really appreciate if you helped me.

Question

Q. Find two consecutive integers whose reciprocals add up to 7/12.

Thanks x

Answer 1

Two consecutive integers are x and x + 1

1 / x + 1 / ( x + 1 ) = 7 / 12

( x + 1 + x ) / [ x ∙ ( x + 1 ) ] = 7 / 12

( 2 x + 1 ) / ( x² + x ) = 7 / 12

12 ∙ ( 2 x + 1 ) = 7 ∙ ( x² + x )

24 x + 12 = 7 x² + 7 x

0 = 7 x² + 7 x - 24 x - 12

0 = 7 x² - 17 x - 12

7 x² - 17 x - 12 = 0

The solutions are x = - 4 / 7 an x = 3

- 4 / 7 isn't integer so x = 3

Proof:

1 / 3 + 1 / 4 = 4 / 12 + 3 / 12 = 7 / 12

Answer 2

thanks, but i have a question. on the 6th step you move the 7 x² + 7 x to the other side but why do you multiply everything by -1?

Answer 3

When you move some variable on other side of equation you must change sign.

24 x + 12 = 7 x² + 7 x

is same

24 x + 12 - ( 24 x + 12 ) = 7 x² + 7 x - ( 24 x + 12 )

0 = 7 x² + 7 x - ( 24 x + 12 )

0 = 7 x² + 7 x - 24 x - 12

7 x² + 7 x - 24 x - 12 = 0