Question

Розв'яжи рівняняння: 1) |x-2|=0 2) |x+3|= -4 3) |x-5|= -5 4) ||x|-2|=0

Answer 1

Ответ:

1) х=-2

2)х=1

3)х=0

4)х=-2

Answer 2

1. |x - 2| = 0: Since the absolute value of any number is always non-negative, the only way for the absolute value to be zero is if the expression inside the absolute value bars is zero itself. So, we have: x - 2 = 0 x = 2

2. |x + 3| = -4: The absolute value of any number is always non-negative, so it cannot be equal to a negative number. Therefore, there are no solutions to this equation.

3. |x - 5| = -5: Similar to the previous equation, the absolute value cannot be equal to a negative number. Hence, there are no solutions to this equation either.

4. ||x| - 2| = 0: Similar to the first equation, the absolute value of any number is zero only if the expression inside the absolute value bars is zero. So, we have: |x| - 2 = 0 |x| = 2

Now, we consider two cases: Case 1: |x| = 2: If |x| = 2, it means that x can be either 2 or -2.

Case 2: -|x| = 2: If -|x| = 2, it means that |x| = -2, which is not possible since the absolute value is always non-negative.

Therefore, the solutions to the equation are x = 2 and x = -2.