Ответы
To solve this inequality, we need to consider the different cases where the absolute value of x + 2 is less than the absolute value of x.
If x is positive, then |x| is equal to x, and we can rewrite the inequality as follows:
|x + 2| < x
Then we can subtract x from both sides of the inequality to get:
|x + 2| - x < 0
We can simplify the left side of the inequality as follows:
|x + 2 - x| < 0
This simplifies to:
|2| < 0
Since the absolute value of 2 is not less than 0, this inequality has no solution in the case where x is positive.
If x is negative, then |x| is equal to -x, and we can rewrite the inequality as follows:
|x + 2| < -x
Then we can add x to both sides of the inequality to get:
|x + 2| + x < 0
We can simplify the left side of the inequality as follows:
|x + 2 + x| < 0
This simplifies to:
|2x + 2| < 0
This inequality has no solution in the case where x is negative.
Therefore, the solution to the inequality |x + 2| < |x| is the empty set, which means that there are no values of x that satisfy the inequality.