Question

The additive inverse of a number, divided by twelve is the same as one less than three times its reciprocal. Find the number

Answer 1

Let the number be x. And it's additive inverse will be -x. Now dividing it by 12 that is -x/12. Now one less than three times it reciprocal is 3/x -1. As they both are equal X/12 = 1 - 3/x. X/12 = x -3/x. X^2 = 12x - 36. X^2 - 12x + 36 = 0. Therefore ( x -6 )^2 = 0. And hence x - 6 = 0. And x = 0

Answer 2

let the required number = x
according to the question,
additive inverse of the  number = -x
condition : -x/12 = 3/x -1
                 -x/12 = (3-x)/ x
                 - x²    = 36 - 12x
                   x² - 12x +36 = 0
                   x ² -6x- 6x + 36 =0
                   x(x - 6) - 6( x - 6) = 0
                   (x-6)(x-6) = 0
                   x = 6
                   therefore , the number is 6.