Question

Даю 20 баллов Решите уравнение: 12 | 4x - 7| = 156 пожалуйста помогите...

Answer 1

Ответ:

x₁ = -1,5 ;       x₂ = 5

Пошаговое объяснение:

12 | 4x - 7| = 156

|4x - 7| = 156:12

|4x - 7| = 13

первое уравнение:

4x - 7 = 13

4x = 13 + 7

4x = 20

x = 5

второе :

4x - 7 = -13

4x = -13 + 7

4x = -6

x = -1,5

Answer 2

Solving the Equation

To solve the equation 12 | 4x - 7| = 156, we can follow these steps:

1. Isolate the Absolute Value - First, isolate the absolute value term by dividing both sides by 12.

2. Solve for x - Once the absolute value is isolated, solve for x by considering both the positive and negative cases.

Solution Steps

1. Isolate the Absolute Value: - Divide both sides by 12 to isolate the absolute value term. - This gives us: |4x - 7| = 13

2. Solve for x: - Consider both the positive and negative cases for the absolute value.

3. Positive Case: - For the positive case, set the expression inside the absolute value equal to the given value (13) and solve for x.

4. Negative Case: - For the negative case, set the expression inside the absolute value equal to the negative of the given value (-13) and solve for x.

Solution

The solutions for the equation 12 | 4x - 7| = 156 are obtained by solving the absolute value equation |4x - 7| = 13 in both the positive and negative cases.

Positive Case: - For the positive case, the solution is: x = 5

Negative Case: - For the negative case, the solution is: x = -2

Therefore, the solutions to the equation are x = 5 and x = -2.