Framing/Writing Linear Inequalities in One Variable

Joan needed $100 to buy a graphing calculator for her math class. Her neighbor will pay her $5 per hour to babysit and her Father gave her $10 for mowing the lawn. Which inequality represents the minimum amount of hours she will need to babysit in order for her to buy her calculator? (Hint 5x)

• 5x + 10 ≥ 100

• 5x - 100 ≥ 10

• 10x + 5 ≤ 100

• 5x + 10 > 100

Translate the sentence into an inequality:

"The difference of eight times a number x and seven is less than or equal to the sum of six times a number x and fifteen"

Ms. Salgado needs to have her car repaired but does not want to spend more than $375 for the repairs. The mechanic says that the part needed for the repair will cost $100 and the labor will cost an additional $40 per hour. Which inequality below represents the greatest number of hours the mechanic can work without exceeding Ms. Salgado’s budget?

• 140x ≤ 375

• 40 + 100x > 225

• 100+ 40x ≤ 375

• 100 + 40x > 375

Sue has at most $200 to spend on softballs and a new softball uniform. The brand of uniform that she wants to buy costs $60. She wants to buy one jersey and spend the rest on softballs. Each softballs costs $10. Which inequality shows the maximum number of softballs that Sue can buy?

• 10s + 60 > 200

• 10s + 60 ≥ 200

• 10s+ 60 < 200

• 10s + 60 ≤ 200

Jonah's Frisbee team had a goal to donate at least 180 items to a charity.All the items combined from Monday & Wednesday are 95 items. What inequality can help solve how many items they have to donate on Friday?

• 95+x≥180

• 56≥56x

• 59>2/x

• 67<45-x

Chris is on vacation at a lake house for the weekend and decided to rent a canoe for the day. They charge him $10 service fee and $38 per hour. He cannot spend more than $200 for the total canoe rental. Create an inequality for this problem.

• 10 + 38x < or = 200

• 10x + 38 < or = 200

• 200 + 38 < or = 10x

A number times 45 decreased by 12 is no more than 117

Justin earned 12 per hour waiting tables then he spent $35 on gas. He now has less than $25 left.

• 12h + 35 < 25

• 12h - 35 < 25

• 12h - 35 ≤ 25

• 12h + 35 ≤ 25

Mark has a lemonade stand and saves $5 of his daily pay to buy a new bike that costs $90. He has already saved $15. Which inequality represents the number of hours, x, that Mark must work to buy the bike?

A number take away 7 is greater than 8

• x - 7 < 8

• x - 7 > 8

• x - 7 < 8

• x - 7 > 8