Question

2(x + 5) < 2 - 2 x,3(2 - x) > 3 - x;​

Answer 1

Ответ:

Пошаговое объяснение:

2x + 10 < 2 - 2x

2x + 2x < 2 -10

4x < - 8

x < -8 : 4

x < -2

x ∈ ( -∞; -2)

6 - 3x > 3 - x

- 3x + x > 3 - 6

-2x > -3

x < -3 : (-2)

x < 1.5

x ∈ ( -∞; 1.5)

Answer 2

To solve the inequalities 2(x + 5) < 2 - 2x and 3(2 - x) > 3 - x, you can follow these steps:

1. Solve the first inequality: 2(x + 5) < 2 - 2x

First, distribute the 2 on the left side: 2x + 10 < 2 - 2x

Now, move all the terms involving x to one side of the inequality and the constants to the other side: 2x + 2x < 2 - 10

Combine like terms: 4x < -8

Divide both sides by 4 (which is a positive number, so the inequality sign doesn't change direction): x < -2

So, the solution to the first inequality is x < -2.

2. Solve the second inequality: 3(2 - x) > 3 - x

First, distribute the 3 on the left side: 6 - 3x > 3 - x

Now, move all the terms involving x to one side of the inequality and the constants to the other side: 6 - 3x + x > 3

Combine like terms: 6 - 2x > 3

Subtract 6 from both sides: -2x > 3 - 6 -2x > -3

Divide both sides by -2, but remember to reverse the inequality sign since you're dividing by a negative number: x < -3/(-2) x < 3/2

So, the solution to the second inequality is x < 3/2.

Now you have the solutions for both inequalities:

1. x < -2
2. x < 3/2

To find the intersection of these solutions, you take the smaller value, which is -2:

x < -2

So, the solution to the system of inequalities is x < -2.