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

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вопрос

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

Positive case: x + 1 < 10
x < 9

Negative case: -(x + 1) < 10
-x - 1 < 10
-x < 11
x > -11

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

Positive case: x + 2 < 11
x < 9

Negative case: -(x + 2) < 11
-x - 2 < 11
-x < 13
x > -13

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

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

Positive case: 3 - x > 0.7
-x > -2.3
x < 2.3

Negative case: -(3 - x) > 0.7
-x + 3 > 0.7
-x > -2.3
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