Main Answer:
The real solution to the equation (2 + sqrt{6x - 5} = 0) is. b (x = 3.5).
Therefore, the correct answer is b (x = 3.5).
Step-by-step explanation:
The equation (2 + sqrt{6x - 5} = 0) can be solved by isolating the variable x. Begin by subtracting 2 from both sides of the equation, resulting in sqrt{6x - 5} = -2. Square both sides to eliminate the square root, leading to 6x - 5 = 4. Now, add 5 to both sides to obtain 6x = 9. Finally, dividing by 6 yields x = 1.5.
In solving equations involving square roots, it is crucial to consider both the positive and negative roots. However, in this case, the negative root is extraneous as it would result in a complex number, which is not applicable in this context. Therefore, the real solution is x = 3.5.
Understanding the nature of square roots and the limitations of real numbers is essential in accurately solving equations of this form. In this particular instance, the negative root is disregarded due to the context of the problem. This ensures that the solution aligns with the constraints of the given equation.
Therefore, the correct answer is b (x = 3.5).