Question

When the reciprocal of three times a number is subtracted from 7, the result is the reciprocal of twice the number. find the number?

Answer 1

To find the number, we set up the equation 7 - 1/(3x) = 1/(2x) and solve for x.

Step-by-step explanation:

To find the number, we need to set up an equation based on the given information.

Let's assume the number is 'x'.

According to the problem, the reciprocal of three times the number is subtracted from 7 and is equal to the reciprocal of twice the number. We can write this as:

7 - 1/(3x) = 1/(2x)

To solve this equation, we can multiply both sides by the common denominator, which is 6x. This will eliminate the fractions.

6x * 7 - 6x * 1/(3x) = 6x * 1/(2x)

42x - 2 = 3

Subtracting 2 from both sides, we get:

42x = 1

Dividing both sides by 42, we find:

x = 1/42

Therefore, the number is 1/42.

Answer 2

Let the number be x. Thus, the reciprocal is
`(1)/(x)`.

Three times x = 3x. Reciprocal of 3x =
`(1)/(3x)`.

Two times x = 2x. Reciprocal of 2x =
`(1)/(2x)`

Given,


`7 - (1)/(3x) = (1)/(2x)`


`(1)/(2x) + (1)/(3x) = 7`


`(3 + 2)/(6x) = 7`

5 = 42x

x =
`(5)/(42)`

Thus, the number is
`(5)/(42)`.