Final answer:
By solving the equation (2x)² = 4.0(1 - x)², we get two potential solutions for x. One of the solutions, x = 2, corresponds to one of the provided selectable answers and falls within the given range for x (1.5 ≤ x ≤ 4.5).
Step-by-step explanation:
To find the value of x, we were provided several pieces of information that describe the properties and behaviors of x. For instance, we know that 1.5 ≤ x ≤ 4.5, meaning x can take any value in that range. We also have an equation that needs to be solved: (2x)² = 4.0(1 - x)². Upon taking the square root of both sides, we get two separate equations, 2x = 2(1 - x) and 2x = -2(1 - x), due to the property of squaring. Solving the former gives us x = 2/3, which does not match any of the options provided. However, solving the latter yields x = 2, which is in the list of possible answers.