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

Answer:

  2/3

Step-by-step 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:

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

The original number is 2/3.

Answer 2

Answer:

n = 1

Step-by-step 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.