Which choice is the solution to the inequality:x2 + 2x–15<0

To solve the inequality x^2 + 2x - 15 < 0, follow these steps:

1. First, factor the quadratic equation. The factors of -15 that add up to 2 are 5 and -3. So, the factored form of the equation is (x - 5)(x + 3) < 0.

2. Set each factor equal to zero and solve for x to find the critical points. This gives you x = 5 and x = -3.

3. Draw a number line and mark these points on it. The intervals created are (-∞, -3), (-3, 5), and (5, ∞).

4. Test a number from each interval in the original inequality. For (-∞, -3), you can use x = -4; for (-3, 5), you can use x = 0; and for (5, ∞), you can use x = 6.

5. If you plug x = -4 into the inequality, you get (-4)^2 + 2(-4) - 15 < 0, which simplifies to 16 - 8 - 15 < 0. This is -7 < 0, which is true. So, the interval (-∞, -3) is part of the solution.

6. If you plug x = 0 into the inequality, you get (0)^2 + 2(0) - 15 < 0, which simplifies to -15 < 0. This is also true. So, the interval (-3, 5) is part of the solution.

7. If you plug x = 6 into the inequality, you get (6)^2 + 2(6) - 15 < 0, which simplifies to 36 + 12 - 15 < 0. This is 33 < 0, which is false. So, the interval (5, ∞) is not part of the solution.

8. Therefore, the solution to the inequality x^2 + 2x - 15 < 0 is x ∈ (-∞, -3) ∪ (-3, 5).