Question

Линейное уравнение с одной переменной, содержащее переменную под знаком модуля. Урок 3 Найди сумму корней уравнения ||5x – 7| – 13| = 5 Ответ: . Назад Проверить ПОМОГИТЕ ПОЖАЛУЙСТА ДАМ 25 БАЛЛОВ ПОЖАЛУЙСТА​

Answer 1

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Answer 2

To find the sum of the roots of a linear equation with one variable that contains the variable under the absolute value sign, we need to solve the equation and then add the values of the roots.

The given equation is ||5x – 7| – 13| = 5.

To solve this equation, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: 5x – 7 ≥ 0

In this case, the absolute value expression becomes 5x – 7, and the equation becomes 5x – 7 – 13 = 5.

Simplifying this equation, we get 5x – 20 = 5.

Adding 20 to both sides, we have 5x = 25.

Dividing both sides by 5, we find x = 5.

Case 2: 5x – 7 < 0

In this case, the absolute value expression becomes -(5x – 7), and the equation becomes -(5x – 7) – 13 = 5.

Simplifying this equation, we get -5x + 7 – 13 = 5.

Combining like terms, we have -5x – 6 = 5.

Adding 6 to both sides, we get -5x = 11.

Dividing both sides by -5, we find x = -11/5.

Therefore, the roots of the equation are x = 5 and x = -11/5.

To find the sum of the roots, we add these values: 5 + (-11/5) = 39/5.

So, the sum of the roots of the equation ||5x – 7| – 13| = 5 is 39/5.

Please let me know if you need any further assistance!