Question

Решите неравентсва с модулям! Последнею Задачу 2|2x-2| < 4 1/3 не надо

Answer 1

Ответ:

Пошаговое объяснение:
2|2х - 2| < 4. 1/3

1)
2(2х -2) < 4. 1/3 , 2х - 2 ≥ 0
4х - 4 < 4. 1/3
4х < 4. 1/3 + 4
4х < 8. 1/3
4х < 25/3
х < 25/3 : 4
х < 25/3 * 1/4
х < 25/12
х < 2. 1/12 ; х ≥ 1

2)
2(2х - 2) < -4. 1/3, 2х - 2 < 0
4х - 4 < -4. 1/3
4х < -4. 1/3 + 4
4х < -1/3
х > -1/3 : 4
х > -1/3 * 1/4
х > -1/12 , х < 1

х1 є [ 1; 2. 1/12)
х2 Є (-1/12; 1)

Ответ: х Є ( -1/12, 2. 1/12)

Answer 2

Solving Equations with Absolute Values

To solve the equation |2x - 2| < 4, we can break it down into two separate inequalities and solve for each case.

1. When (2x - 2) is positive: - This occurs when 2x - 2 > 0. - Solving for x: 2x - 2 < 4.

2. When (2x - 2) is negative: - This occurs when 2x - 2 < 0. - Solving for x: -(2x - 2) < 4.

Let's solve each of these inequalities separately.

Case 1: When (2x - 2) is positive

When 2x - 2 > 0, we have: - 2x - 2 < 4 - Adding 2 to both sides: 2x < 6 - Dividing by 2: x < 3

So, for this case, the solution is x < 3.

Case 2: When (2x - 2) is negative

When 2x - 2 < 0, we have: - -(2x - 2) < 4 - Multiplying by -1 (which reverses the inequality): 2x - 2 > -4 - Adding 2 to both sides: 2x > -2 - Dividing by 2: x > -1

So, for this case, the solution is x > -1.

Combining the Solutions

Combining the solutions from both cases, we get: - -1 < x < 3

Therefore, the solution to the inequality |2x - 2| < 4 is -1 < x < 3.