3x² +12x-36 ≤0 нужен срочный ответ помогите пооожалуйста​

Ответ:To solve this inequality:

1. Factor out the common factor 3.

        3(x² + 4x - 12) ≤ 0

2. Factor the expression inside the parentheses using the product-sum method.

        3(x + 6)(x - 2) ≤ 0

3. Find the critical values by setting each factor equal to zero and solving for x.

        x + 6 = 0 → x = -6

        x - 2 = 0 → x = 2

4. Plot the critical values on a number line.

                -6                    2

5. Test a point in each of the three intervals that are created on the number line by the critical values.

        For x < -6, choose x = -7: 3(-1)(-9) ≤ 0    --> True

        For -6 < x < 2, choose x = 0: 3(6)(-12) ≤ 0  --> True

        For x > 2, choose x = 3: 3(27)(6)  > 0       --> False

6. Determine the solution to the inequality.

        The inequality is satisfied when x ≤ -6 or 2 ≤ x.

        So the solution can be written as:

                            x ≤ -6  or  x ≥ 2.

Пошаговое объяснение: