Each ride costs $2.75$ dollars. For $r$ rides, should you add $2.75$ once, or multiply $2.75$ by $r$?

The problem asks for when the monthly pass is less expensive than paying per ride. Which side of the inequality should represent the pass cost, and which side should represent the pay-per-ride cost?

In Desmos, type y1 = 96. This horizontal line represents the constant cost of using the monthly pass, no matter how many rides you take.

Type y2 = 2.75x. This line represents the total cost of paying per ride, where $x$ is the number of rides and the cost increases as $x$ increases.

Look for the $x$-values where the $y2$ graph (paying per ride) is above the $y1$ graph (monthly pass). Those $x$-values show when paying per ride costs more than the pass, which corresponds to the inequality where the fixed pass cost is less than the per-ride cost expression.

For $r$ bus rides:

• Cost with the monthly pass is always $96$ dollars (it does not depend on $r$).
• Cost without the pass is $2.75$ dollars per ride, so the total is $2.75r$ dollars.

We want the number of rides $r$ for which buying the monthly pass is less expensive than paying per ride.

• Let "cost with pass" be on the left.
• Let "cost without pass" be on the right.
• "Pass is less expensive than paying per ride" becomes:

So in symbols we have: $\text{pass cost} < \text{per-ride cost}$.

Now replace each phrase with the expression you found:

• Pass cost is $96$.
• Per-ride cost is $2.75r$.

So the inequality becomes

This matches answer choice A) $96 < 2.75r$.