let the number be x
1/(x-4) = 2(1/x)
solve for x
1/(x-4) = 2(1/x)
solve for x
The reciprocal of a number is just 1 divided by that number. So, if we let the number be "x", the reciprocal of "x" would be 1/x.
According to the problem, the reciprocal of 4 less than the number is three times the reciprocal of the same number. So, mathematically, we can write it as:
1/(x - 4) = 3 * (1/x)
Now, let's solve this equation...or maybe we could call a math magician to solve it. Do you happen to know any?
But seriously, let's continue:
Multiplying both sides of the equation by x * (x - 4) to get rid of the denominators, we get:
x = 3 * (x - 4)
Now let's distribute:
x = 3x - 12
Subtracting x from both sides:
0 = 2x - 12
Adding 12 to both sides:
12 = 2x
Dividing both sides by 2:
x = 6
So, the number is 6.
Let's assume the number is x.
According to the problem, the reciprocal of 4 less than the number is three times the reciprocal of the same number.
The reciprocal of a number x is 1/x. So, the reciprocal of 4 less than the number is 1/(x - 4).
According to the problem, this reciprocal is three times the reciprocal of the same number. Therefore, we can write the equation as:
1/(x - 4) = 3 * (1/x)
Now, we can solve this equation to find the value of x.
Multiplying both sides of the equation by (x - 4) * x to eliminate the denominators:
(x - 4) * x * [1/(x - 4)] = (x - 4) * x * [3 * (1/x)]
Cancelling out the common factors:
x = 3 * (x - 4)
Expanding the right side of the equation:
x = 3x - 12
Bringing all the terms with x to one side of the equation:
x - 3x = -12
Simplifying:
-2x = -12
Dividing both sides of the equation by -2:
x = -12 / -2
Simplifying further:
x = 6
Therefore, the number is 6.