Question

if 1/2 is added to the reciprocal of a number, the result is 1 less than twice the reciprocal; of the original number. Find the number.

Answer 1

n = 1

Explanation:

Represent the number with n.

Then: reciprocal of this numer is 1/n.

1/2 added to this reciprocal comes to 1/n + 1/2, and this is equal to

2(1/n) - 1.

We must simplify this equation and solve for n:

Use the LCD 2n:

2 + n = 4 - 1, or 2 + n = 3, or n = 1.

Answer 2

2/3

Explanation:

Let x represent the number. Then its reciprocal (the reciprocal of the original number) is 1/x

1/2 + 1/x . . . . . 1/2 added to the reciprocal of a number

2/x -1 . . . . . . . 1 less than twice the reciprocal of the original number

We want these expressions to be equal:

`(1)/(2)+(1)/(x)=(2)/(x)-1\\\\(3)/(2)=(1)/(x)\qquad\text{add 1-(1/x)}\\\\x=(2)/(3)\qquad\text{multiply by 2x/3}`

The original number is 2/3.