Solving Two-Step Inequalities Answers
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
What is the first step in solving c Negative 5 x minus one-sixth greater-than-or-equal-to three-halves ?
Solve –9.4 1.7x + 4.2.
Monica has $20. She needs to buy a gallon of milk that costs $2.50. She also wants to buy yogurt, which costs $1.20 a cup. Which inequality can you use to find the number of cups of yogurt Monica can buy?
Monica can buy cups of yogurt.
14
Tony’s class needs more than $500 for the school dance. So far, they have raised $200. They plan to have a car wash, charging $8 a car, to raise more money. Tony solved the inequality 8x + 200 500, and determined that if they wash 37 cars, they will have enough money. Is he correct? Explain.
No, Tony is not correct. When you solve the inequality 8x + 200 ≥ 500, you first subtract 200 from both sides to get 8x ≥ 300. Then, dividing by 8 gives x ≥ 37.5. Since the class must wash a whole number of cars, they need to wash at least 38 cars to meet their goal. 37 cars would only raise 37 * 8 + 200 = $496, which is less than $500.
Sample Response: No, Tony is not correct. Solving the inequality tells us that x is greater than or equal to 37.5. Since the class must wash a whole number of cars, they need to wash at least 38 cars. Which did you include in your solution? Check all that apply.The solution to the inequality is x 37.5.For this situation, only whole number solutions make sense.Tony needs to round up to 38.
The first step in solving the inequality is to add 47.5 to both sidessubtract 47.5 from both sidesmultiply both sides by 47.5divide both sides by 47.5.
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 $10, otherwise he will take a bus. Carl is 15 miles from home. Explain how to write and solve an inequality to determine if Carl will take the taxi or a bus.
To determine if Carl will take the taxi, let x represent the number of miles. The inequality for the cost is 0.50x + 3 < 10. To solve, first subtract 3 from both sides of the inequality to get 0.50x < 7. Next, divide both sides by 0.50 to find that x < 14. This means Carl can only afford the taxi if the trip is less than 14 miles. Since Carl is 15 miles from home, he will take the bus.
Review Jamie’s work. What was her error?
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