Think about how the phrase “at least 8 hours” compares the total hours to 8. Should the total be less than 8, greater than 8, or could it be equal to 8 as well?

Once you have an expression for the total hours, decide whether that expression should be connected to 8 with $\le$, $\ge$, $<$, or $>$ based on “at least 8.”

Notice whether the situation involves a sum of hours or a difference of hours. Which makes sense for a total?

In Desmos, enter each answer choice as it is, one at a time, for example: h + s <= 8. Desmos will treat $h$ and $s$ as the horizontal and vertical axes and shade the region that satisfies the inequality.

For each inequality you graph, look at which points $(h,s)$ are shaded. Remember, each point represents a possible combination of hours: $h$ hours at the hospital and $s$ hours at the shelter. You want the region where the sum of hours is 8 or more.

Compare the story—"total volunteer time is at least 8 hours"—to the shaded region from each option. The correct inequality will shade exactly the combinations where the total hours are 8 or greater, and not shade combinations where the total is less than 8.

The volunteer splits time between two places: the hospital and the shelter.

• Let $h$ be the hours at the hospital.
• Let $s$ be the hours at the shelter.

The total hours volunteered each week is the sum of these:

• Total hours $= h + s$.

In inequalities, common phrases translate like this:

• “At least 8” means 8 or more, so use $\ge 8$.
• (By contrast, “at most 8” would mean 8 or less, so you would use $\le 8$.)

So the condition from the problem is that the total hours must be at least 8: total $\ge 8$.

We already know:

• Total hours is $h + s$.
• That total must be at least 8, so it must satisfy $\ge 8$.

Putting these together gives the inequality

This matches choice D, so the correct answer is $h + s \ge 8$.