2 | x + 5 | + | x - 11 | - 30 > 0

Предыдущий
вопрос Следующий
вопрос

To solve this inequality, we will need to break it down into different cases based on the absolute values.

Case 1: x + 5 ≥ 0 and x - 11 ≥ 0
In this case, both absolute values are positive. So, the inequality becomes:
2(x + 5) + (x - 11) - 30 > 0
2x + 10 + x - 11 - 30 > 0
3x - 21 - 30 > 0
3x - 51 > 0
3x > 51
x > 17

Case 2: x + 5 ≥ 0 and x - 11 < 0
In this case, the first absolute value is positive and the second one is negative. So, the inequality becomes:
2(x + 5) - (x - 11) - 30 > 0
2x + 10 - x + 11 - 30 > 0
x + 1 - 30 > 0
x - 29 > 0
x > 29

Case 3: x + 5 < 0 and x - 11 ≥ 0
In this case, the first absolute value is negative and the second one is positive. So, the inequality becomes:
-2(x + 5) + (x - 11) - 30 > 0
-2x - 10 + x - 11 - 30 > 0
-x - 21 - 30 > 0
-x - 51 > 0
-x > 51
x < -51

Case 4: x + 5 < 0 and x - 11 < 0
In this case, both absolute values are negative. So, the inequality becomes:
-2(x + 5) - (x - 11) - 30 > 0
-2x - 10 - x + 11 - 30 > 0
-3x + 1 - 30 > 0
-3x - 29 > 0
-3x > 29
x < -9.67

Therefore, the solution to the inequality is:
-51 < x < -9.67 or x > 29.