Solving Inequalities in One Variable Word Problems

Which inequality is represented by the words " no more than" or "at most"?

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• ≤
• ≥

Which inequality is represented by the words " more than"?

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• >
• ≤
• ≥

Which inequality is represented by the words " at least"?

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• >
• ≤
• ≥

Johnny earns $15 per hour dog walking. He wants to earn at least $105 to buy a new bike. Which inequality represents how long Johnny needs to work to afford his new bike?

• 15h ≤ 105

• 15h > 105

• 15h < 105

• 15h ≥ 105

Yellow Cab Taxi charges a $1.75 flat rate in addition to $0.65 per mile. Katie has no more than $10 to spend on a taxi ride.

Which inequality best describes how many miles Katie can ride in this taxi?

• 1.75 + 0.65m < 10

• 1.75 + 0.65m > 10

• 1.75m + 0.65 < 10

• 1.75m + 0.65 > 10

The Starlight Bowling Alley charges $6 to rent shoes and $8 per game. Cameron has only $42 to spend. Which inequality represents this scenario if “x” represents the number of games Cameron can play?

• 6x + 8 ≥ 42

• 8x + 6 ≤ 42

• 6x + 8 > 42

• 8x + 6 < 42

Katie wants to have at least $200 in her bank account by the end of the month. She currently has $25 in her bank account. Katie makes $12 for each dog that she walks.

Which inequality could help you find how many dogs Katie would have to walk to reach her goal?

• 25 - 12x ≥ 200

• 25 + 12x ≥ 200

• 13x ≥ 200

• 25 + 12x < 200

A limo driver needs to make more than $450 in one day. He charges a rental fee of $375 plus $0.85 per mile. What inequality represents the number of miles, x, he would have to drive to reach his goal?

• 0.85x + 375 > 450

• 0.85x + 375 < 450

• 0.85 + 375x > 450

• 0.85 + 375x < 450

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?

• 5x + 10 ≥ 100

• 5x - 100 ≥ 10

• 10x + 5 ≤ 100

• 5x + 10 > 100

The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour but offers a $55 discount for clients who pay ahead of time.

The committee wants to keep the total cost under $600. Which inequality represents the maximum amount of hours the DJ will play at the dance if the committee pays ahead of time?

• 125x + 55 < 600

• 125x - 55 > 600

• 125x + 55 > 600

• 125x - 55 < 600