Question

[x = π + 3/2]

[2x = π + 3]
[2x(π - 3) = (π + 3)(π - 3)]
[2π x - 6x = π² - 9]
[9 - 6x = π² - 2π x]
[9 - 6x + x² = π² - 2π x + x²]
[(3 - x)² = (π - x)²]
[3 - x = π - x]
[π = 3]
Which line was incorrect, resulting in the final answer to be incorrect?
A. (2x(π - 3) = (π + 3)(π - 3))
B. (2π x - 6x = π² - 9)
C. (9 - 6x = π² - 2π x)
D. [(3 - x)² = (π - x)²]

Answer 1

The incorrect step was D, which falsely equates (π - x)² with (3 - x)² and ultimately leads to the wrong conclusion that π equals 3.

Step-by-step explanation:

The incorrect step in the provided sequence of equations is D. [(3 - x)² = (π - x)²]. When squaring the expressions (3 - x) and (π - x), the result implies they are equal to each other. However, this only means that the absolute values of (3 - x) and (π - x) are equal, not the expressions themselves. The correct next step should consider both the positive and negative roots when taking the square root of both sides to solve for x.

Error in step D led to the incorrect conclusion that π = 3, which is false as π is an irrational number approximately equal to 3.14159...