Real-Life Linear Inequalities: Graphing and Solving Challenges

A school is planning a field trip and needs at least 30 students to attend. If 5 students have already signed up, how many more students need to sign up? Write and graph the inequality that represents this situation.

• 10

• 15

• 20

• 25

A local gym has a maximum capacity of 50 people. If there are currently 20 members working out, how many more can enter? Write the inequality and graph it.

• 25

• 40

• 30

• 15

A farmer has 100 meters of fencing to create a rectangular pen for animals. If the length of the pen is represented by x, what is the inequality for the width y? Graph the inequality.

• y > 50 - x

• 0 < y < 50 - x

• 0 < y < 100 - x

• y < 0

A concert hall can seat a maximum of 200 people. If 150 tickets have been sold, how many more tickets can be sold? Write the inequality and graph it.

• 100

• 75

• 50

• 25

A store is having a sale where each item must cost less than $20. If a shirt costs x dollars, write the inequality and graph it to show the possible prices.

• x > 20

• x ≤ 20

• x = 20

• x < 20

A car rental company charges a base fee of $30 plus $15 for each day the car is rented. If a customer has a budget of $120, write the inequality for the number of days d they can rent the car and graph it.

• d ≤ 8

• d ≤ 5

• d ≤ 6

• d ≤ 4

A pizza shop sells large pizzas for $15 each. If a customer wants to spend no more than $60, write the inequality for the number of pizzas p they can buy and graph it.

• p ≤ 4

• p ≤ 5

• p ≤ 3

• p < 4

A student needs to score at least 75% on a test to pass. If the test has 40 questions, how many questions must they answer correctly? Write the inequality and graph it.

• 40

• 35

• 25

• 30

A factory produces gadgets and can produce a maximum of 500 gadgets per day. If they produced 300 gadgets today, how many more can they produce? Write the inequality and graph it.

• 400

• 300

• 100

• 200

A charity event aims to raise at least $1,000. If they have already raised $450, how much more do they need to raise? Write the inequality and graph it.

• They need to raise at least $600 more.

• They need to raise at least $450 more.

• They need to raise at least $550 more.

• They need to raise at least $700 more.