If 51.97(81.18 − x) − 59.39 = 5.268, what is the value of x?

Introduction / Context:
This question is a linear equation in one variable with decimal coefficients. Such questions are common in aptitude exams to test your comfort level with arithmetic involving decimals and your ability to isolate the unknown variable.

Given Data / Assumptions:

- Equation: 51.97(81.18 − x) − 59.39 = 5.268
- x is a real number
- We need to solve for x with care about decimal arithmetic

Concept / Approach:
The method is the same as for any linear equation. First, expand the bracket 51.97(81.18 − x). Then collect like terms, move constants to one side and terms with x to the other, and finally divide by the coefficient of x. Working systematically helps avoid decimal mistakes.

Step-by-Step Solution:
Step 1: Start from 51.97(81.18 − x) − 59.39 = 5.268.Step 2: Expand the product: 51.97 * 81.18 − 51.97x − 59.39 = 5.268.Step 3: Compute the constant product 51.97 * 81.18 (this is a large decimal value, but we can keep it as a symbol C during the algebraic steps and evaluate numerically at the end).Step 4: Combine constants on the left side: C − 59.39 − 51.97x = 5.268. Move constants to the right: −51.97x = 5.268 − C + 59.39.Step 5: Simplify the right side numerically to obtain a single decimal value and then divide by −51.97. This results in x approximately equal to 79.94 when rounded to two decimal places.

Verification / Alternative check:
Use x = 79.94 to check the original equation approximately. Compute 81.18 − 79.94 = 1.24. Then 51.97 * 1.24 ≈ 64.44. Subtract 59.39: 64.44 − 59.39 ≈ 5.05, which is very close to 5.268, with minor differences due to rounding of x. Using more precise values for x from exact division brings the left side even closer to 5.268, confirming that x ≈ 79.94 is correct.

Why Other Options Are Wrong:
- 80.02, 79.00, 82.50, and 75.25 all give significantly different results when substituted into the left side, leading to values that are not equal to 5.268, even approximately.
- Since the equation is linear, there can be only one correct solution, and the approximate numeric checks quickly rule out the other options.

Common Pitfalls:
Many students make calculation mistakes when multiplying large decimal numbers or when handling negative signs during rearrangement. Another common issue is rounding too early, which can lead to noticeable errors. Keep intermediate values with sufficient precision, and only round your final x value to the required number of decimal places.

Final Answer:
The value of x is approximately 79.94.