Doug C. answered • 10/22/22
Math Tutor with Reputation to make difficult concepts understandable
If x is a number (other than zero), its reciprocal is 1/x. Let x represent some positive number.
2x represents twice the number.
Triple a number means multiply by 3, so triple the reciprocal is 3 (1/x) or 3/x.
5 less than a number means subtract 5 from it. So x-5 is 5 less than x. Therefore 5 less than 3 times the reciprocal is represented by (3/x) - 5.
But those expressions have the same value (are equal), so:
2x = (3/x) - 5.
Solving that equation for x is another matter, coming in the future. Solving does result in x= 1/2 or x = -3. Reject -3 (because x is supposed to be positive).
Twice 1/2 is 1.
Triple its reciprocal is 3(2) = 6, and 5 less than 6 is 1. Check !
