X²+4x-21>0

To solve the inequality x² + 4x - 21 > 0, we can use the method of quadratic inequalities.

Step 1: Factor the quadratic equation x² + 4x - 21 = 0. (x - 3)(x + 7) = 0

Step 2: Find the critical points where the equation equals zero. x - 3 = 0, x = 3 x + 7 = 0, x = -7

Step 3: Plot these critical points on a number line. -7 --- 3

Step 4: Choose a test point in each interval and substitute into the inequality to determine if it satisfies the inequality. Let's choose x = -8 (interval -∞ to -7): (-8)² + 4(-8) - 21 = 64 - 32 - 21 = 11 > 0

Let's choose x = 0 (interval -7 to 3): 0² + 4(0) - 21 = -21 < 0

Let's choose x = 4 (interval 3 to ∞): 4² + 4(4) - 21 = 16 + 16 - 21 = 11 > 0

Step 5: Determine the solution based on the sign of the test points. The inequality is satisfied when x < -7 or x > 3.

So, the solution to the inequality x² + 4x - 21 > 0 is x < -7 or x > 3.