Let's analyze and interpret the given inequalities step by step.
Given conditions:
1. \( y \geq 3x + 3 \)
2. \( y \leq 2x + 10 \)
3. \( y > y \)
Let's break this down:
1. \( y \geq 3x + 3 \):
This condition suggests that \( y \) is at least \( 3x + 3 \).
2. \( y \leq 2x + 10 \):
This condition indicates that \( y \) is at most \( 2x + 10 \).
3. \( y > y \):
This condition suggests that \( y \) must be greater than \( y \), which is a contradiction.
This is because a variable cannot be greater than itself. Since \( y > y \) cannot be satisfied under any circumstances, it invalidates all possible values of \( x \) and \( y \).
Thus, considering the conditions provided, no values of \( x \) can satisfy all three inequalities simultaneously.
Therefore, the interval for \( x \) in this case is:
[tex]\[ \text{No solution as the inequality } y > y \text{ cannot be satisfied.} \][/tex]
