Question

Решите систему неравенств:

Answer 1

Смотри фото...............................................

Answer 2

Solving the System of Inequalities

To solve the system of inequalities, let's consider the given inequalities:

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

We will solve each inequality separately and then find the intersection of their solution sets.

# Solving Inequality 1: 8 + 4x > 0

To solve the first inequality, we can start by isolating the variable x.

1. Subtract 8 from both sides of the inequality: 8 + 4x - 8 > 0 - 8 Simplifying, we get: 4x > -8

2. Divide both sides of the inequality by 4: (4x)/4 > (-8)/4 Simplifying, we get: x > -2

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

# Solving Inequality 2: 4 - 3x > -8

To solve the second inequality, we can follow a similar process.

1. Add 8 to both sides of the inequality: 4 - 3x + 8 > -8 + 8 Simplifying, we get: -3x + 12 > 0

2. Subtract 12 from both sides of the inequality: -3x + 12 - 12 > 0 - 12 Simplifying, we get: -3x > -12

3. Divide both sides of the inequality by -3. Note that when dividing by a negative number, the inequality sign flips: (-3x)/(-3) < (-12)/(-3) Simplifying, we get: x < 4

Therefore, the solution to the second inequality is x < 4.

# Intersection of Solution Sets

To find the intersection of the solution sets, we need to find the values of x that satisfy both inequalities.

From the first inequality, we have x > -2, and from the second inequality, we have x < 4.

The values of x that satisfy both inequalities are between -2 and 4, excluding -2 and 4. In interval notation, the solution set is (-2, 4).

Therefore, the solution to the system of inequalities is x ∈ (-2, 4).

Please note that the solution is based on the given system of inequalities. If there are any additional constraints or information, please provide them for a more accurate solution.