Final answer:
To solve the inequality 2x^2 -5x -3 ≥ 0 algebraically, we can find the x-values where the quadratic expression is equal to zero and determine the intervals where it is positive or negative. The solution is x ≤ x1 or x ≥ x2.
Step-by-step explanation:
To solve the inequality 2x^2 -5x -3 ≥ 0 algebraically, we can find the x-values where the quadratic expression is equal to zero and determine the intervals where it is positive or negative.
Step 1: Set 2x^2 -5x -3 = 0
Step 2: Solve for x by factoring or using the quadratic formula:
Step 3: Use a sign chart or test points to determine the intervals where the expression is positive or negative:
- Interval (-∞, x1): Function is negative
- Interval (x1, x2): Function is positive
- Interval (x2, ∞): Function is negative
Therefore, the solution to the inequality 2x^2 -5x -3 ≥ 0 is x ≤ x1 or x ≥ x2.