Question

Помогите решить неравенство: (x+6)(x-8)/2x-7<или=0 Пожалуйста))

Answer 1

Решим неравенство методом интервалов: 
$(x+6)(x-8)/ (2x-7) \leq 0$ 
Нули: -6, 8, 3.5
Нанесем их на прямую:          Промежутки: От минус бесконечности до - 6 и от (3,5, 8]

Answer 2

Solving the Inequality:

To solve the given inequality (x+6)(x-8)/2x-7 <= 0, we can follow these steps:

1. Find the critical points by setting the numerator and denominator equal to zero. 2. Use these critical points to create intervals on the number line. 3. Test a value from each interval in the original inequality to determine the solution set.

Step 1: Finding Critical Points:

The critical points are the values that make the numerator or the denominator equal to zero.

The critical points for the given inequality are: - Numerator: x = -6 and x = 8 - Denominator: x = 7/2

Step 2: Creating Intervals:

We can use these critical points to create intervals on the number line: - Interval 1: (-∞, -6) - Interval 2: (-6, 7/2) - Interval 3: (7/2, 8) - Interval 4: (8, +∞)

Step 3: Testing Intervals:

Now, we can test a value from each interval in the original inequality to determine the solution set.

- For Interval 1 (-∞, -6): - Let's test x = -7: - Substituting x = -7 into the inequality gives: ((-7+6)(-7-8))/(2(-7)-7) = (-1 * -15)/(-14-7) = 15/-21 - Since 15/-21 > 0, this interval is not part of the solution set.

- For Interval 2 (-6, 7/2): - Let's test x = 0: - Substituting x = 0 into the inequality gives: ((0+6)(0-8))/(2(0)-7) = (6 * -8)/(-7) = -48/-7 - Since -48/-7 < 0, this interval is part of the solution set.

- For Interval 3 (7/2, 8): - Let's test x = 5: - Substituting x = 5 into the inequality gives: ((5+6)(5-8))/(2(5)-7) = (11 * -3)/(3) = -33/3 - Since -33/3 < 0, this interval is part of the solution set.

- For Interval 4 (8, +∞): - Let's test x = 9: - Substituting x = 9 into the inequality gives: ((9+6)(9-8))/(2(9)-7) = (15 * 1)/(11) = 15/11 - Since 15/11 > 0, this interval is not part of the solution set.

Conclusion:

The solution set for the inequality (x+6)(x-8)/2x-7 <= 0 is: (-6, 7/2] U [8, +∞)