Final answer:
To solve the inequality x^2 + 3x - 18 ≤ 0, we factor the quadratic to get (x + 6)(x - 3) ≤ 0. By finding the roots and testing intervals, we determine the solution set for the inequality is -6 ≤ x ≤ 3.
Step-by-step explanation:
To solve the inequality x2 + 3x - 18 ≤ 0 algebraically, we first need to find the factors of the quadratic equation. Factoring the quadratic, we get:
(x + 6)(x - 3) ≤ 0
The solutions for the equation x2 + 3x - 18 = 0 are x = -6 and x = 3.
To solve the inequality, we determine the intervals to test within the solution.
We have three intervals to test due to the roots of the quadratic:
- Interval 1: x < -6
- Interval 2: -6 ≤ x ≤ 3
- Interval 3: x > 3
By testing these intervals with values within the inequality, we find that the inequality holds true for Interval 2.
Therefore, the solution set for the inequality is -6 ≤ x ≤ 3.