Question

Найти все значение икс при которых верно равенство: 1) |х|=0 ; 2) |х|=2 ; 3) |х|=1/3 ; 4) |х-1|=2

Answer 1

Ответ:

1) при х= 0

2) при х = 2 или х = -2

3) при х =1/3 или при х = -1/3

4) при х = 3 или при х = -1

Answer 2

Ответ:

Пошаговое объяснение:

|х|=0

x=0

|х|=2

x=±2

|х|=1/3

x=±1/3

|х-1|=2

x-1=±2

x-1=2  x-1=-2

x=3    x= -1

Answer 3

1. |x| = 0

The absolute value of any number is always non-negative, and it is equal to zero only when the number itself is zero. Therefore, for the equation |x| = 0, the only solution is x = 0.

2. |x| = 2

For the equation |x| = 2, there are two possible solutions: x = 2 and x = -2. The absolute value of both these numbers is 2.

3. |x| = 1/3

There are no real solutions for the equation |x| = 1/3. The absolute value of any real number is always non-negative, so it can't be equal to a negative number like 1/3.

4. |x - 1| = 2

To solve this equation, we need to consider two cases:

Case 1: x - 1 = 2 Solving this equation, we get x = 3.

Case 2: -(x - 1) = 2 Solving this equation, we get -x + 1 = 2, which simplifies to -x = 1. Multiplying both sides by -1, we find x = -1.

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