| х + 1 | < 10 , | х + 2 | < 11 , | 3 - х | > 0,7

Предыдущий
вопрос Следующий
вопрос

To solve these absolute value inequalities, we need to consider both the positive and negative cases for each inequality.

Positive case: x + 1 < 1
x < 9

Negative case: -(x + 1) < 1
-x - 1 < 1
-x < 1
x > -11

Combining both cases, we get -11 < x < 9

Positive case: x + 2 < 1
x < 9

Negative case: -(x + 2) < 1
-x - 2 < 1
-x < 1
x > -13

Combining both cases, we get -13 < x < 9

First, we need to split this inequality into two parts:

Positive case: 3 - x > 0.
-x > -2.
x < 2.3

Negative case: -(3 - x) > 0.
-x + 3 > 0.
-x > -2.
x < 2.3

Combining both cases, we get x < 2.3 or x > 2.3

In conclusion, the solution to the system of absolute value inequalities is -13 < x < 2.3 or 9 < x