Question

(x+3)(x-8)≥0 Решите неравенство

Answer 1

Ответ: 8
(8+3)×(8-8)>0

Answer 2

To solve this inequality, we need to first find the values of x that make the expression (x+3)(x-8) equal to 0, as these will be the critical points that separate the intervals where the inequality is either positive or negative.

So, we set (x+3)(x-8) = 0 and solve for x:

(x+3)(x-8) = 0 x+3 = 0 or x-8 = 0 x = -3 or x = 8

Therefore, the critical points are -3 and 8.

Next, we can test each interval defined by these critical points by picking a test point within each interval and evaluating the expression (x+3)(x-8) at that point. If the result is positive, then the entire interval is part of the solution. If the result is negative, then the interval is not part of the solution.

Let's start with the interval (-∞,-3). If we pick a test point x = -4, then (x+3)(x-8) = (-1)(-12) = 12, which is positive. Therefore, the entire interval (-∞,-3) is part of the solution.

Next, we consider the interval (-3,8). If we pick a test point x = 0, then (x+3)(x-8) = (3)(-8) = -24, which is negative. Therefore, the interval (-3,8) is not part of the solution.

Finally, we consider the interval (8,∞). If we pick a test point x = 9, then (x+3)(x-8) = (12)(1) = 12, which is positive. Therefore, the entire interval (8,∞) is part of the solution.

Putting it all together, the solution to the inequality (x+3)(x-8) ≥ 0 is:

x ≤ -3 or x ≥ 8