Final answer:
To solve the inequality x^2 - 3x >= 0, factor the quadratic to x(x - 3) >= 0 and test the intervals determined by the critical points, x = 0 and x = 3. The correct solution is B. (x >= 0) or (x <= 3).
Step-by-step explanation:
To solve the inequality x^2 - 3x \geq 0, we need to find the values of x that make the expression non-negative. The first step is to factor the quadratic expression, which can be written as x(x - 3) \geq 0. This indicates that the product of x and (x - 3) should be greater than or equal to zero.
We set each factor equal to zero to find the critical points: x = 0 and x = 3. These values divide the number line into intervals that we can test in the inequality: (-\infty, 0), (0, 3), and (3, \infty). By testing a number from each interval in the original inequality, we find that the solution set consists of the intervals where the expression is non-negative. As a result, the correct answer is B. (x \geq 0) or (x \leq 3), since for x in these intervals, the inequality holds true.