Question

Найти ''x'': ||x|-1|<3

Answer 1

Ответ:
[-4;4]
Вот, легко

Answer 2

To find the possible values of ''x'' that satisfy the inequality ||x| - 1| < 3, we'll need to consider two cases since the absolute value can result in both positive and negative values. Let's break it down:

Case 1: x is positive or zero (x ≥ 0) In this case, |x| is equal to x, so the inequality becomes: |x - 1| < 3

Case 2: x is negative (x < 0) In this case, |x| is equal to -x, so the inequality becomes: |-x - 1| < 3

Now, let's solve both cases:

Case 1: x is positive or zero (x ≥ 0) |x - 1| < 3

If x - 1 is positive (x > 1): x - 1 < 3 x < 3 + 1 x < 4

If x - 1 is negative (0 ≤ x < 1): 1 - x < 3 1 - 3 < x -2 < x

So, the possible values for Case 1 are 0 ≤ x < 1 and x < 4.

Case 2: x is negative (x < 0) |-x - 1| < 3

If -x - 1 is positive (-x > 1): -x - 1 < 3 -x < 3 + 1 -x < 4 Since we have a negative number on the left side, we need to reverse the inequality sign: x > -4

If -x - 1 is negative (-x ≤ 1): x + 1 < 3 x < 3 - 1 x < 2

So, the possible values for Case 2 are -4 < x < 0 and x < 2.

Now, we need to find the intersection of the solutions from both cases:

The overlapping range is: 0 ≤ x < 1 and x < 2.

Thus, the final solution for ''x'' is 0 ≤ x < 1.