A taxi charges a flat rate of $3.00, plus an additional $0.50 per mile. Carl will only take the taxi home if the cost is under $

Unfortunately, Carl cannot take the taxi, primarily due to financial constraints. To demonstrate this, we begin by forming an inequality to tackle the issue. Let x signify the mileage. The relevant inequality is 0.50x + 3 < 10. If we substitute x with 15, it becomes ($0.50 * 15) + $3 < $10. It’s crucial to use a less than sign (<) because Carl requires the fare to be below, not equal to, the limit. We calculate by multiplying 0.50 and 15, yielding $7.5. Substituting that value back into the inequality, we have $7.5 + $3 < $10. A simple addition reveals that Carl falls short by 50 cents, confirming his inability to afford the taxi fare, and thus he must take the bus.

Define x as the distance in miles. This scenario can be expressed with the inequality 0.5x + 3 < 10, where x corresponds to the miles traveled. To solve this, begin by subtracting 3 from each side, followed by dividing everything by 0.5. The outcome indicates x < 14, meaning Carl can cover less than 14 miles, though he is 15 miles away from his destination; therefore, he will opt for a bus instead.