Question

(3x + 4) (2x - 5) > 0;​

Answer 1

Ответ:

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Объяснение:

Answer 2

To determine the values of x that satisfy the inequality (3x + 4)(2x - 5) > 0, we can use the concept of interval notation and test the intervals created by the critical points.

Let's break down the problem step by step:

1. Find the critical points: Set each factor equal to zero and solve for x: 3x + 4 = 0 => x = -4/3 2x - 5 = 0 => x = 5/2

   The critical points are x = -4/3 and x = 5/2.

2. Create intervals: These critical points divide the number line into three intervals:

   Interval 1: (-∞, -4/3) Interval 2: (-4/3, 5/2) Interval 3: (5/2, ∞)

3. Test each interval: Choose a test point within each interval and substitute it into the inequality.

   For Interval 1, let's choose x = -2: (3(-2) + 4)(2(-2) - 5) = (-2)(-9) = 18 > 0

   For Interval 2, let's choose x = 0: (3(0) + 4)(2(0) - 5) = (4)(-5) = -20 < 0

   For Interval 3, let's choose x = 3: (3(3) + 4)(2(3) - 5) = (13)(1) = 13 > 0

4. Determine the solution: The intervals where the inequality (3x + 4)(2x - 5) > 0 holds are: Interval 1: (-∞, -4/3) Interval 3: (5/2, ∞)

   Therefore, the solution to the inequality is: x ∈ (-∞, -4/3) ∪ (5/2, ∞)