Question

||||x|-2|-2|-2|=2. ​

Answer 1

Ответ:

Пошаговое объяснение:

|||| x | - 2| - 2 | - 2|  = 2;

||| x | - 2| - 2 | - 2  = 2;

||| x | - 2| - 2 | = 4

|| x | - 2| - 2 = 4

|| x | - 2|  = 6

| x | - 2 = 6;   | x | = 8;  x = - 8;  8

Ответ:  x = - 8;  x = 8

Answer 2

To solve the equation |||x|-2|-2|-2| = 2, we need to consider the different cases for the absolute value expressions.

1. Case: |x|-2 is positive In this case, the equation simplifies to |x|-2-2-2=2. | x | - 6 = 2

Now, isolate the absolute value expression: | x | = 2 + 6 | x | = 8

So, for this case, we have two possible solutions:

1. x = 8 (since |8| = 8)
2. x = -8 (since |-8| = 8)

2. Case: |x|-2 is negative In this case, the equation simplifies to -(|x|-2-2-2) = 2. -| x | + 6 = 2

Now, isolate the absolute value expression: -| x | = 2 - 6 -| x | = -4

This case doesn't give us any valid solutions because the absolute value of any number cannot be negative. Thus, there are no solutions for this case.

Final Solution: The solutions to the equation |||x|-2|-2|-2| = 2 are x = 8 and x = -8.