Question

(х+8)(х-5)>0 решите неравенство используя метод интервалов

Answer 1

х+8=0 х=-8

х-5=0  х=5

       +                         -                +

----------------(-8)-----------5--------->

Ответ:(-∞;-8);(5;+∞)

 

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Answer 2

Solving the Inequality (х + 8)(х - 5) > 0 using Interval Method

To solve the inequality (х + 8)(х - 5) > 0 using the interval method, we can follow these steps:

1. Find the Critical Points: - The critical points are the values of x where the expression (х + 8)(х - 5) equals 0.

- The critical points are x = -8 and x = 5.

2. Create Intervals: - We need to create intervals on the number line based on the critical points.

- The critical points divide the number line into three intervals: (-∞, -8), (-8, 5), and (5, +∞).

3. Test Intervals: - We will test a value from each interval in the inequality (х + 8)(х - 5) > 0 to determine the solution set.

- For the interval (-∞, -8), we can test x = -9. - For the interval (-8, 5), we can test x = 0. - For the interval (5, +∞), we can test x = 6.

4. Determine the Solution: - Based on the results of the tests, we can determine the solution set for the inequality (х + 8)(х - 5) > 0.

Solution Steps

1. Find the Critical Points: - The critical points are x = -8 and x = 5.

2. Create Intervals: - The critical points divide the number line into three intervals: (-∞, -8), (-8, 5), and (5, +∞).

3. Test Intervals: - For the interval (-∞, -8): (x + 8)(x - 5) = (-9 + 8)(-9 - 5) = (-1)(-14) = 14 > 0. - For the interval (-8, 5): (0 + 8)(0 - 5) = (8)(-5) = -40 < 0. - For the interval (5, +∞): (6 + 8)(6 - 5) = (14)(1) = 14 > 0.

4. Determine the Solution: - Based on the tests, the solution set for the inequality (х + 8)(х - 5) > 0 is x < -8 or x > 5.

Therefore, the solution to the inequality (х + 8)(х - 5) > 0 using the interval method is x < -8 or x > 5.