THe reciprocalof two more than a number is 3/4 of the reciprocal of the number itself. What is the number?

Question

THe reciprocalof two more than a number is 3/4 of the reciprocal of the number itself. What is the number?

Answer 1

1/(x + 2) = 3/(4x)
4x = 3x + 6
x = 6

Answer 2

Rewrite that as an equation and you get 1/(x + 2) = 3/4 * 1/x = 3/4x. Divide 3/4x by 3/3 and you get 1/(x +2) = 1/(4x/3). That means (x + 2) must be equal to (4x/3).

So write a new equation: x + 2 = 4x/3. Multiply both sides by 3: 3x + 6 = 4x. Subtract 3x from each side: x = 6.

Plug it into the original equation to check it: 1/(6 + 2) = 3/4 (1/6); 1/8 = 3/4*1/6; 1/8 = 3/24. This is true, so the answer is correct.

The number is 6.

Answer 3

let x be the number
1/(x + 2) = 3/4x

proportion - to solve use cross product:

3(x + 2) = 4x
3x + 6 = 4x
so x = 6