Final answer:
To solve the rational inequality ((4-2x))/(2x+3)≤0, identify zeros of the numerator and points where the expression is undefined, test the intervals around these points, and express the solution in interval notation: [-⅓, 2].
Step-by-step explanation:
To solve the rational inequality ((4-2x))/(2x+3)≤0, we first need to find the values of x where the expression is equal to zero, or undefined. The expression is equal to zero when the numerator is zero, which is at x=2. The expression is undefined when the denominator is zero, which is at x=-⅓. We then use these points to test the intervals they create on the number line. The intervals are (-∞, -⅓), (-⅓, 2), and (2, ∞).
Checking a point in each interval, we see where the expression is less than or equal to zero. We summarize this in interval notation as the solution: [-⅓, 2].