Solving and Writing Inequalities

Daniel can spend no more than $40 at the fair. If admission into the fair is $10 and the rides cost $1.50 each, which inequality represents the greatest number of rides Daniel can go on?

• 10x + 1.50 ≥ 40
• 1.50x + 10 ≤ 40
• 1.50x + 10 <40
• 10x + 1.50 < 40

The temperature in the ice rink must stay below 50°F. This morning, the temperature was 71°F. The ice rink runs a cooling device that can decrease the temperature by 3.5° every hour. Which inequality shows how long it will take for the temperature to fall below 50°F?

• 50 + 3.5x < 71
• 71 - 3.5x < 50
• 71 - 3.5x ≤ 50
• 71 + 3.5x < 50

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. Which inequality shows the number of tickets they must sale to reach their goal?

• 300x + 10 ≥ 2000
• 10x + 300 ≤ 2000
• 10x + 300 > 2000
• 300 + 10x ≥ 2000

The vet told Casey that her dog should weigh at most 70 lbs. Her dog weighs 106 pounds, so Casey set a goal that he would lose 4 pounds per week. Which inequality represents the number of weeks it take for Casey's dog to reach 70 lbs?

• 106 - 4x ≤ 70
• 70 + 4x ≤ 106
• 4x - 106 ≥ 70
• 106 - 4x< 70

It costs Amy $0.20 to send a text message.  She has already spent $5 in text messages this month.  If she has a total of $12 that can spend this month on text messages, write and solve an inequality that will give the greatest number of text messages that she can send.

• 0.20x + 5 = 12;
  85 text messages
• 0.20(5x) = 12; 
  12 text messages
• 0.20x + 5 ≤ 12;
  x ≤ 35 
• 0.20x + 5 ≥ 12;
  x ≥ 35

Which word problem represents the inequality:
x + 32 ≥ 80
(Show work by writing down inequality clue words.)

• Janine's goal is to earn at least $80 for soccer camp.  She has earned $32 so far.  How much more does she need to earn?
• Janine made more than 80 points during the basketball season.  She made 32 points the first five games.  How much did she score the rest of the games?
• Janine scored above an 80 on her math homework.  But, she turned her work in late and was deducted 32 points.  What did she make after the deduction?

Match the inequality to the word problem.

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. How many dogs would Katie have to walk to reach her goal of $200?

• 25 - 12x ≥ 200
• 25 + 12x ≥ 200
• 13x ≥ 200
• 25 + 12x > 200

Pheobe has $500 in a savings account at the beginning of the summer. She wants to have at least $200 in account by the end of the summer. She withdraws $25 each week for food, clothes, and movie tickets. Write an inequality that represents Pheobe's situation.

• 200+25w ≥ 500
• 500-25w ≥ 200
• 500+25w ≤ 200
• 200-25w ≤ 500

Benton is going shopping. He wants to spend less than $250. If he bought shirts that are $30 each and a pair of shoes for $120, how many shirts did he buy? Which inequality represents this situation?

• 30x + 120 > 250
• 30x + 120 < 250
• 30x + 120 ≥ 250
• 30x + 120 ≤ 250

Dale has $25 to spend at a carnival. If the admission to the carnival is $4 and the rides cost $1.50 each, which inequality represents the greatest number of carnival rides Dale can go on?

• 1.5x + 4 ≤ 25
• 1.5x + 25 > 4
• 4x + 1.5 ≤ 25
• 25x + 1.5 > 4