Question

Решите системы рациональных неравенств неравенств 4(9х+3)-9(4х+3)>3 (х-2) (х+9)<0

Answer 1

−15>3⇒−18>04(9x+3)−9(4x+3)=Раскрытие скобок:36x+12−36x−27=12−27=Приведение подобных:−15
−15>3⇒−18>0
Ответ: x∈∅ , т.е. решений нет.
Т.к. первое неравенство не имеет решений, то и данная система неравенств не имеет решений.

Answer 2

Solving the System of Rational Inequalities

To solve the system of rational inequalities, we'll start by simplifying and solving each inequality separately.

1. Simplify the First Inequality: The first inequality is: 4(9x + 3) - 9(4x + 3) > 3.

Let's simplify this inequality step by step.

First, distribute the terms: 4(9x + 3) - 9(4x + 3) > 3 36x + 12 - 36x - 27 > 3 12 - 27 > 3

Now, simplify the inequality: -15 > 3

As -15 is not greater than 3, this inequality has no solution.

2. Simplify the Second Inequality: The second inequality is: (x - 2) + (x + 9) < 0.

Let's simplify this inequality step by step.

Combine like terms: x - 2 + x + 9 < 0 2x + 7 < 0

Now, solve for x: 2x < -7 x < -7/2

So, the solution for the second inequality is x < -7/2.

Conclusion

The system of rational inequalities has no solution due to the first inequality, and the solution for the second inequality is x < -7/2.