Framing/Writing Linear Inequalities

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

Matilda needs at least $112 to buy a new dress. She has already saved $40. She earns $9 an hour babysitting. Select the inequality below that matches the problem.

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

Chance set a goal of saving at least $200 in his savings account.

He currently has $40 in his account. If he saves $5 per week, how many weeks will it take him to reach his goal?

Write the inequality to the problem.

• 5c + 40 ≥ 200

• 5c + 40 ≤ 200

• 40c + 5 ≥ 200

• 40c + 5 ≤ 200

The members of Carver Middle School's Junior Beta Club need to raise at least $2000 to attend their national convention.

· They raised $300 with their last fundraiser and decide to host a school talent show to raise the rest.

· They plan to charge $10 for each ticket.

Let t represent the number of tickets they must sell to reach their goal.

• 300x + 10 ≥ 2000

• 10x + 300 ≤ 2000

• 10x + 300 > 2000

• 300 + 10x ≥ 2000