Mastering Compound Inequalities: Solve and Graph Challenges

1. A store sells pencils for between $0.50 and $1.50 each. If you want to buy at least 5 pencils, how much will you spend in total? Solve the compound inequality and graph the solution.

• $2.50 to $7.50

• $0.00 to $10.00

• $1.00 to $5.00

• $3.00 to $8.00

2. The temperature in a city is expected to be between 60°F and 80°F this weekend. If the temperature is represented by 't', write and solve the compound inequality for 't'.

• 60 > t > 80

• t < 60

• t > 80

• 60 ≤ t ≤ 80

3. A swimming pool requires a water level between 3 feet and 5 feet. If the current water level is represented by 'w', write the compound inequality and determine if the pool is at a safe level.

• The pool is safe if w is exactly 4 feet.

• The pool is safe if w is less than 3 feet.

• The pool is at a safe level if w is between 3 and 5 feet inclusive.

• The pool is safe if w is greater than 5 feet.

4. A student needs to score between 70% and 90% on a test to maintain their grade. If 'x' represents the score, write the compound inequality and find the range of scores that will keep the grade intact.

• 60 <= x <= 80

• 75 < x < 85

• 50 <= x <= 100

• 70 <= x <= 90

5. A car can travel between 25 and 35 miles per gallon of gas. If you plan to drive 200 miles, how many gallons of gas will you need? Solve the compound inequality and graph the results.

• Between 5.71 and 8 gallons of gas.

• 3 to 4 gallons of gas.

• 10 to 12 gallons of gas.

• 4 to 6 gallons of gas.

6. A concert venue has a seating capacity between 500 and 800 people. If 's' represents the number of tickets sold, write the compound inequality and determine if the concert can proceed without exceeding capacity.

• The concert can proceed with 800 tickets sold.

• The concert cannot proceed if fewer than 501 tickets are sold.

• Yes, the concert can proceed without exceeding capacity if the number of tickets sold is between 501 and 799.

• The concert can only proceed if 500 tickets are sold.

7. A runner wants to maintain a pace between 8 and 10 minutes per mile. If 'p' represents the pace, write the compound inequality and find the range of paces that the runner can achieve.

• 8 <= p <= 10

• 6 <= p <= 8

• p < 8 or p > 10

• 10 < p < 12

8. A recipe requires between 2 and 4 cups of flour. If you have 'f' cups of flour, write the compound inequality and determine if you have enough flour to make the recipe.

• Check if 2 <= f <= 4 to determine if you have enough flour.

• The recipe requires exactly 3 cups of flour, so check if f = 3.

• Check if f < 2 or f > 4 to determine if you have enough flour.

• You need at least 5 cups of flour to make the recipe.

9. A student must read between 5 and 10 books this semester to pass a reading challenge. If 'b' represents the number of books read, write the compound inequality and find the possible values for 'b'.

• 4, 5, 6, 7

• The possible values for 'b' are 6, 7, 8, 9.

• 10, 11, 12, 13

• 1, 2, 3, 4

10. A bike can travel between 15 and 25 miles per hour. If you ride for 2 hours, how far can you travel? Solve the compound inequality and graph the possible distances.

• 30 to 50 miles

• 35 to 55 miles

• 25 to 45 miles

• 20 to 40 miles