In elementary algebra, the sum of a real number x and four times its reciprocal 1/x is equal to 5. If x is non zero, what is the value of the original number x that satisfies this equation?

Introduction / Context:
This question tests basic algebraic manipulation involving reciprocals and quadratic equations. Many aptitude exams include problems where a number and its reciprocal appear together, so learning a systematic way to handle such equations is very useful.

Given Data / Assumptions:

• x is a real number and x is not equal to zero.
• x + 4 * (1 / x) = 5.
• We must find the numerical value of x that satisfies this equation.

Concept / Approach:
The main idea is to clear the denominator by multiplying through by x, which converts the equation with a reciprocal into a quadratic equation. Once we obtain a quadratic, we can factorise it or use standard techniques to find the roots and then choose the correct one from the options.

Step-by-Step Solution:
Start with x + 4 * (1 / x) = 5. Multiply both sides by x (which is non zero): x * x + 4 = 5x. This gives x^2 + 4 = 5x. Rearrange to standard quadratic form: x^2 - 5x + 4 = 0. Factorise: x^2 - 5x + 4 = (x - 1)(x - 4) = 0. So the possible values are x = 1 or x = 4. Check both values in the original equation x + 4 / x = 5. For x = 1: 1 + 4 / 1 = 5, which is valid. For x = 4: 4 + 4 / 4 = 4 + 1 = 5, which is also valid. Both 1 and 4 satisfy the equation, but only 4 appears in the given options.
Verification / Alternative check:
We verified by direct substitution that x = 1 and x = 4 both satisfy the equation. As aptitude questions usually ask you to choose from listed options, we simply select the root that is available in the options, which is x = 4.

Why Other Options Are Wrong:
Option b (5): 5 + 4 / 5 = 5 + 0.8 = 5.8, which is not equal to 5.
Option c (6): 6 + 4 / 6 = 6 + 2 / 3 = 6.666..., not equal to 5.
Option d (7): 7 + 4 / 7 is greater than 7 and clearly not equal to 5.
Option e (8): 8 + 4 / 8 = 8.5, not equal to 5.

Common Pitfalls:
A common mistake is to forget to multiply every term by x when clearing the denominator or to make sign errors when rearranging to quadratic form. Another error is to stop after finding both roots but not checking which root is actually present in the options. Always substitute the roots back into the original equation and then compare with the options provided.

Final Answer:
Hence, the number that satisfies the given condition and appears in the options is 4.