Let 'h' represent the number of hours that Charles will work. Since he wants to work for at least six hours, then we have the following inequality:
![6\le h](https://img.qammunity.org/2023/formulas/mathematics/high-school/uyt2zimpvt0sy3s0vx0ch0pfgl5ybofcys.png)
but he also must work fewer than 16 hours this week, then the next inequality is:
![h\le16](https://img.qammunity.org/2023/formulas/mathematics/high-school/otij0s7c7vs3wvp54fm71o0etv6ty9r37g.png)
then, combining the inequalities, we have:
![6\le h\le16](https://img.qammunity.org/2023/formulas/mathematics/high-school/wry257hac6f840x17ev9kz8zlut85of97q.png)