Question

Ребят помогите пожалуйста 20 баллов. Вот решите график с модулями, все хорошенько распишите пожалуйста. Вот : |5x-10|+x ПОМОГИТЕ Пожалуйста

Answer 1

Раскрываем модуль: 5х + 10 + х => 6х + 10.

Answer 2

Solving the Equation Involving Absolute Value

To solve the equation |5x-10| + x, we need to consider two cases: when the expression inside the absolute value is positive and when it's negative. Let's start by solving for both cases.

Case 1: (5x-10) is Positive

When 5x-10 is positive, the absolute value expression simplifies to (5x-10). Therefore, the equation becomes: 5x-10 + x = 0

Case 2: (5x-10) is Negative

When 5x-10 is negative, the absolute value expression simplifies to -(5x-10), which is equivalent to -5x+10. Therefore, the equation becomes: -5x+10 + x = 0

Now, let's solve each case separately.

Solving Case 1: (5x-10) is Positive

We'll solve the equation 5x-10 + x = 0 for this case.

5x-10 + x = 0 6x - 10 = 0 6x = 10 x = 10/6 x = 5/3

Solving Case 2: (5x-10) is Negative

We'll solve the equation -5x+10 + x = 0 for this case.

-5x+10 + x = 0 -4x + 10 = 0 -4x = -10 x = -10/-4 x = 5/2

Conclusion

The solutions to the equation |5x-10| + x are: x = 5/3 and x = 5/2