Framing/Writing Linear Inequalities in Two Variables from Word Problem

A number multiplied by 2 is no more than 12

• x > 12

• x < 12

• 2x ≤ 12

• 2x > 12

Ross and Chandler go to Taco Land and order sodas for a total of $3.50. They also want to order some tacos (of course), which cost $1.75 each. If they have $20, how many tacos can they buy? Which inequality best represents the situation.

• 3.50 + 1.75t > 20

• 1.75 + 3.50t ≤ 20

• 3.50 + 1.75t ≥ 20

• 1.75t + 3.50 ≤ 20

A new tree you just planted will grow to be at most 35 feet tall. If it is currently 6 feet tall. Which of the following inequalities could be used to find all all the possible values of how many more feet, f, will it grow?

• 6 + x ≥ 35

• 6 + x > 35

• 6 + x < 35

• 6 + x ≤ 35

Top Golf charges $12 for each hour. You can spend no more than $60. Which of the following inequalities could help you solve for all the possible hours, h, that you can golf for?

• 12x < 60

• 12x ≤ 60

• 12x > 60

• 12x ≥ 60

• 30x < 330 + 50x

• 50x > 330 + 30x

• 30x > 330 + 50x

• 50x < 330 + 30x

• 2.5v + 5 < 5v

• 2.5v + 5 > 5v

• 7.5v < 5v

• 7.5v > 5v

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Cody’s Gym charges a $15 fee to join and $30 per month. Tyler’s Gym charges a $30 fee to join and $20 per month. Write an inequality that could be used to determine after how many months Tyler’s gym would be a better deal.

• 30 + 20x < 15 + 30x

• 30x + 20 < 15x + 30

• 30 + 20x > 15 + 30x

• 30x + 20 > 15x + 30

Kim is using two mobile networks. Network one charges RM0.30 for every minute of call and network two charges RM0.38 for every minute of call. Kim spends at least RM68 monthly for calls. Which of the following inequalities is best to represent Kim's situation?

• 0.30x + 0.38y < 68

• 0.30x + 0.38y > 68

• 0.30x + 0.38y ≤ 68

• 0.30x + 0.38y ≥ 68

Alvin, a mechanic, earns $17 for every oil change, x, he performs and $77 for every tune-up, y. He needs to earn over $1,400 today to be able to pay the rent for his business and still have some money left over.

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

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