Question

РЕШИТЕ УРАВНЕНИЯ 1) |x|=7 2) |x|=-4 3) |-x|=8,4

Answer 1

Ответ:

1)х = -7 и 7

2) х принадлежит пустому множеству

3) х = -8,4 и 8.4

Пошаговое объяснение:

Answer 2

Ответ:
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Answer 3

1. |x| = 7:

To solve this equation, we need to consider two cases: when x is positive and when x is negative.

Case 1: x is positive. If x is positive, then |x| is equal to x. So we have: x = 7

Case 2: x is negative. If x is negative, then |x| is equal to -x. So we have: -x = 7

To find the solution for each case, let's solve the equations separately:

Case 1: x = 7 The solution in this case is x = 7.

Case 2: -x = 7 To isolate x, we multiply both sides of the equation by -1: x = -7

Therefore, the solutions to the equation |x| = 7 are x = 7 and x = -7.

2. |x| = -4:

The absolute value of any number is always non-negative. Therefore, there is no solution to the equation |x| = -4.

3. |-x| = 8.4:

Since the absolute value of any number is always non-negative, we can rewrite the equation as follows:

|-x| = 8.4 |x| = 8.4

We can solve this equation using the same approach as in the first question:

Case 1: x is positive. If x is positive, then |x| is equal to x. So we have: x = 8.4

Case 2: x is negative. If x is negative, then |x| is equal to -x. So we have: -x = 8.4

To find the solution for each case, let's solve the equations separately:

Case 1: x = 8.4 The solution in this case is x = 8.4.

Case 2: -x = 8.4 To isolate x, we multiply both sides of the equation by -1: x = -8.4

Therefore, the solutions to the equation |-x| = 8.4 are x = 8.4 and x = -8.4.