Question: Solve each system of inequalities.
{
m > 9
m > 10
m < 12
}
1. **State the problem:** We need to solve the system of inequalities:
$$m > 9$$
$$m > 10$$
$$m < 12$$
2. **Understand the system:** The solution must satisfy all three inequalities simultaneously.
3. **Analyze each inequality:**
- $$m > 9$$ means $$m$$ is greater than 9.
- $$m > 10$$ means $$m$$ is greater than 10.
- $$m < 12$$ means $$m$$ is less than 12.
4. **Combine the inequalities:** Since $$m$$ must be greater than both 9 and 10, the stricter condition is $$m > 10$$.
5. **Write the combined solution:**
$$10 < m < 12$$
6. **Final answer:** The solution set is all $$m$$ such that $$m$$ is greater than 10 and less than 12.