Sample Response: Let the variable x be the number of miles. Then the problem can be modeled with the inequality 0.5x + 3 < 10, in which x is the number of miles. To solve, first subtract 3 from each side, then divide each side by 0.5. The solution is x < 14. Carl can travel less than 14 miles, but he lives 15 miles away, so he will take a bus, not the taxi. Which did you include in your solution? Check all that apply.The inequality representing the situation is 0.5x + 3 < 10.Use inverse operatio
Answer
A
The inequality representing the situation is 0.5x + 3 < 10.
B
Use inverse operations and properties of inequality to solve.
C
Find that x < 14.
D
Carl lives 15 miles from home, so he will take a bus.
Explanation
The response sets up the inequality 0.5x + 3 < 10, so it includes the model in choice A. It says to subtract 3 and divide by 0.5, which uses inverse operations to solve, as in choice B, and gives x < 14, as in choice C. Finally, it compares the 14-mile limit with Carl’s 15-mile distance and concludes he will take a bus, as in choice D.
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