2x + 3 ≥ 7
2x ≥ 7 - 3
2x ≥ 4
x ≥ 4 / 2
x ≥ 2
2x + 9 > 11
2x > 11 - 9
2x > 2
x > 1
Those are your two inequalities, now we must find one that satisfies both. Combine them together you get:
1 < 2 ≤ x
That last inequality becomes your answer.
x ≥ 2 makes both statements true.