A linear inequality can describe a weekly total that must meet a limit. If time is divided between two places, add the hours to find the total; subtracting would compare the places instead. Then translate the minimum into a symbol that allows both the exact limit and greater amounts. A direct translation needs no graph, even with Desmos open.
Hints
- Hint 1
The hours at the two places are parts of one weekly total. To find all the time spent volunteering, what operation combines the hospital hours and shelter hours?
- Hint 2
In an inequality, the bar under a symbol means “or equal to.” Spending exactly 8 hours meets the pledge. Which direction must the symbol point to allow more than 8 as well?
Step-by-step
Translate the total and the minimum
Step 1Write the weekly total
No Desmos needed. This is a direct translation of a weekly total. The hospital hours and shelter hours are parts of the same week, so add them:
Subtracting would compare the hours at the two places, not count all the volunteer hours.
- Step 2
Set the minimum
The pledge says at least hours, so the total can be or more:
The bar in includes exactly ; would set a maximum instead. The volunteer's combined hospital and shelter hours must be at least each week. Choice D.