Question

Решить систему неравенств:

Answer 1

$4x \geq 5$
$- 2x \geq -2$

$x \geq 1.25$
$x \leq 1$
Ответ: система не имеет решений

Answer 2

Solving the System of Inequalities

To solve the system of inequalities, we will consider each inequality separately and find the values of x that satisfy each one. Then, we will find the intersection of the solution sets to determine the values of x that satisfy both inequalities.

The given system of inequalities is as follows:

1. 8 + 4x > 0 2. 4 - 3x > -8

Let's solve each inequality step by step:

Inequality 1: 8 + 4x > 0

To solve this inequality, we need to isolate x on one side of the inequality sign. Here's how we can do it:

8 + 4x > 0

Subtract 8 from both sides:

4x > -8

Divide both sides by 4:

x > -2

Therefore, the solution to the first inequality is x > -2.

Inequality 2: 4 - 3x > -8

To solve this inequality, we will follow a similar process:

4 - 3x > -8

Add 3x to both sides:

4 > -8 + 3x

Subtract 4 from both sides:

8 > 3x

Divide both sides by 3:

8/3 > x

Therefore, the solution to the second inequality is x < 8/3.

Now, let's find the intersection of the solution sets for both inequalities:

The solution to the system of inequalities is the values of x that satisfy both x > -2 and x < 8/3. In other words, the solution is the values of x that are greater than -2 and less than 8/3.

Therefore, the final solution to the system of inequalities is -2 < x < 8/3.

Please let me know if you need any further clarification or assistance!