Which choice is the solution to the inequality:x2 – 4x–5 > 0

To solve the inequality x^2 - 4x - 5 > 0, follow these steps:

1. First, factor the quadratic equation. The equation factors to (x - 5)(x + 1) = 0.

2. Set each factor equal to zero and solve for x to find the critical points. This gives you x = 5 and x = -1.

3. Draw a number line and mark these points on the line. The points divide the number line into three intervals: (-∞, -1), (-1, 5), and (5, ∞).

4. Test a number from each interval in the original inequality to determine which intervals are part of the solution.

   For (-∞, -1), let's pick x = -2. Substituting -2 into the inequality gives (-2)^2 - 4*(-2) - 5 = 4 + 8 - 5 = 7, which is greater than 0. So, (-∞, -1) is part of the solution.

   For (-1, 5), let's pick x = 0. Substituting 0 into the inequality gives 0^2 - 4*0 - 5 = -5, which is not greater than 0. So, (-1, 5) is not part of the solution.

   For (5, ∞), let's pick x = 6. Substituting 6 into the inequality gives (6)^2 - 4*6 - 5 = 36 - 24 - 5 = 7, which is greater than 0. So, (5, ∞) is part of the solution.

5. Therefore, the solution to the inequality x^2 - 4x - 5 > 0 is x < -1 or x > 5.