1. căn x + 1 > 3
To solve this inequality, we need to isolate the variable x.
First, subtract 1 from both sides:
căn x > 2
Next, square both sides of the inequality:
x > 4

2. căn 4 - x ≥ 6
To solve this inequality, we need to isolate the variable x.
First, subtract 4 from both sides:
căn -x ≥ 2
Since the square root of a negative number is not defined in the real number system, there is no solution for this inequality.

3. căn 2x + 1 ≥ 3
To solve this inequality, we need to isolate the variable x.
First, subtract 1 from both sides:
căn 2x ≥ 2
Next, square both sides of the inequality:
2x ≥ 4
Divide both sides by 2:
x ≥ 2

4. căn 3x + 2 > căn 11
To solve this inequality, we need to isolate the variable x.
First, square both sides of the inequality:
3x + 2 > 11
Subtract 2 from both sides:
3x > 9
Divide both sides by 3:
x > 3