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?

• 5x + 10 ≥ 100

• 5x - 100 ≥ 10

• 10x + 5 ≤ 100

• 5x + 10 > 100

Translate the sentence into an inequality. twice the sum of a number and 3 is at least 18.

• 2(x + 3) < 18

• 2x + 3 < 18

• 2(x + 3) ≥ 18

• 2x + 3 ≥ 18

Jeff bought a bottle of water for $2. He also bought some hot dogs for $3 each. Jeff did not spend more than $14 on the hot dogs and the bottle of water. Which inequality can be used to find h, the number of hot dogs that Jeff could have bought?

• 3h − 2 ≤ 14

• 3h + 2 ≤ 14

• 3h − 2 ≥ 14

• 3h + 2 ≥ 14

10 is at most a number 'x' minus 13

Mathematical Equivalence

ON

An elevator can only hold a maximum of 1500 pounds. If equipment weighs 945 pounds, how much more pounds of supplies (x) can be put on the elevator? Which inequality would represent this situation?  

• x - 945 > 1500
• x + 945 > 1500
• x - 945 ≤ 1500
• x + 945 ≤ 1500

Penelope is going to the carnival to ride the rides. It costs $20 to get into the carnival and ride tickets are $0.50 each. Write an equation that represents this scenario if she can spend no more than $35 in all.

• .50x + 20 ≥ 35

• .50x < 35

• .50x + 20 ≤ 35

• .50x - 20 = 35

Gideon wants to save at least $550 in 10 weeks. He already has $50 saved.

Which of the following inequalities could Gideon use to find "x", the least amount of money he needs to save every week?

• 550 > 10x + 50

• 550 < 10x + 50

• 550 > 10x + 50

• 550 < 10x + 50

Save your answer to this question, you will need it for the next one!

The elementary school is having a fall carnival. Admission into the carnival is $3 and each game inside the carnival costs $0.25. You have $10.00 to spend at this carnival. Which of the inequalities below correctly models this information if "g" represents the number of games you play?

• $3g+0.25\le10$

• $3+0.25g\le10$

• $3g+0.25\ge10$

•  $3+0.25g\ge10$ 

• Esteban charges $1.25 for gasoline plus $6.50 per hour for mowing lawns. What is x, the number of hours he has to mow lawns to earn more than $50?

• Esteban spends $6.50 on supplies for a lemonade stand and sells each cup of lemonade for $1.25. What is x , the number of cups of lemonade Esteban must sell to earn a profit of more than $50?

• Esteban has a balance of $6.50 in his savings account and deposits $1.25 each week. What is x , the number of weeks Esteban must deposit $1.25 in order to have a balance of more than $50 in his savings account?

• Esteban earns 1.25% interest on the balance in his checking account and has to pay a monthly charge of $6.50. What is , the balance that Esteban must have in his checking account in order to have an ending balance greater than $50 after interest and fees?

Translate:
5 less than the product of 7 and s is no more than 14

• 7s - 5 
  ≤ 14
• 5 - 7 + s 
  ≥ 14
• 7(s - 5) 
• 5 - 7s 
  ≠ 14