The sum of the reciprocal of a number and 4 equals 9. What is the number?

To solve the problem, we start with the given equation based on the information provided. The problem states that the sum of the reciprocal of a number and 4 equals 9. We can express this relationship mathematically.

Let's denote the number as ( x ). The reciprocal of the number is ( \frac{1}{x} ). According to the problem, we can set up the equation:

[

\frac{1}{x} + 4 = 9

]

Next, we can isolate the reciprocal term by subtracting 4 from both sides of the equation:

[

\frac{1}{x} = 9 - 4

]

This simplifies to:

[

\frac{1}{x} = 5

]

To find ( x ), we take the reciprocal of both sides:

[

x = \frac{1}{5}

]

Thus, the solution indicates that the number is ( \frac{1}{5} ). This matches with the provided answer.

The reasoning behind this solution is grounded in basic algebraic manipulation, specifically the handling of equations involving fractions and basic arithmetic operations. The concept of reciprocals plays a key role in determining the value of (