Solving and Graphing Real-Life Inequalities for 8th Grade

1. Sarah has twice as many apples as Tom. If Tom has x apples, write an inequality to represent the situation if Sarah has at least 10 apples. Solve for x and graph the inequality.

• x < 5

• x = 7

• x > 10

• x >= 5

2. A concert hall can hold a maximum of 500 people. If tickets are sold for $20 each and the cost of organizing the concert is $3000, write an inequality to find the minimum number of tickets that must be sold to break even. Solve for the variable and graph the inequality.

• x >= 200

• x >= 250

• x >= 150

• x >= 100

4. A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If a customer wants to spend no more than $50, write an inequality to represent the maximum number of miles they can drive. Solve for the variable and graph the inequality.

• m ≤ 80

• m ≤ 90

• m ≤ 120

• m ≤ 100

5. A gardener has 20 feet of fencing to create a rectangular garden. If the length is represented by x and the width is represented by y, write an inequality to represent the perimeter of the garden. Solve for y in terms of x and graph the inequality.

• y ≤ 10 - x

• y = 10 - 2x

• y < 10 + x

• y ≥ 10 - x

6. A school is planning a field trip and has a budget of $1200. If each student pays $15 and there are x students, write an inequality to find the maximum number of students that can attend. Solve for x and graph the inequality.

• x <= 80

• x <= 100

• x <= 75

• x <= 60

8. A bike shop sells mountain bikes for $300 and road bikes for $400. If a customer wants to spend no more than $1200, write an inequality to represent the maximum number of each type of bike they can buy. Solve for the number of mountain bikes in terms of road bikes and graph the inequality.

• x ≤ 3 - (1/2)y

• x ≤ 5 - (2/3)y

• x ≤ 4 - (4/3)y

• x ≤ 2 - (3/4)y

9. A student is saving money for a new laptop that costs $800. If they save $50 a week, write an inequality to represent how many weeks it will take to save enough money if they already have x dollars saved. Solve for x and graph the inequality.

• w >= (800 - x) / 50

• w < (800 - x) / 50

• w > (800 - x) / 50

• w <= (800 + x) / 50

10. A factory produces x items per hour and needs to produce at least 1000 items in a day. If the factory operates for 8 hours, write an inequality to represent the situation. Solve for x and graph the inequality.

• x < 125

• x <= 100

• x > 150

• x >= 125