Question

||x-2|-1|=3 Пожалуйста, помогите

Answer 1

1) x≥2

|x-2-1|=3
|x-3|=3
           a) x≥3 ⇒ x-3=3  ⇒ x=6
           б) 2≤x<3  ⇒ -x+3=3   ⇒x=0 не удовлетворяет промежутку

2) x<2
|-x+2-1|=3
|1-x|=3
            a) 1≤x<2 ⇒ -1+x=3  ⇒ x=4 не удовлетворяет
            б)   x<1   ⇒ 1-x=3  ⇒ x=-2
               
      
Ответ х=6 и х=-2

Answer 2

Solving the Equation ||x-2|-1|=3

To solve the equation ||x-2|-1|=3, we can break it down into two separate equations based on the absolute value.

1. When (x-2) is positive or zero: - In this case, the equation becomes: (x-2)-1=3 - Solving for x, we get: x-2-1=3, which simplifies to x-3=3, and then x=6.

2. When (x-2) is negative: - In this case, the equation becomes: -(x-2)-1=3 - Solving for x, we get: -x+2-1=3, which simplifies to -x+1=3, and then -x=2, and finally x=-2.

So, the solutions for the equation ||x-2|-1|=3 are x=6 and x=-2.

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Conclusion

The solutions for the equation ||x-2|-1|=3 are x=6 and x=-2.