Compound Inequalities Worksheets Grade 7

1. 2(x + 3) > 8 and 3x - 5 ≤ 10
2. A rectangular garden is drawn on a coordinate grid with vertices at (0, 0), (18, 0), (18, 14), and (0, 14). A triangular flower bed is placed inside the garden with vertices at (0, 0), (10, 0), and (0, 7). The gardener wants to plant grass in the remaining area. However, a path for a fence must also be built along the inside of the garden such that the distance from the left and bottom edges is at least 2 meters and at most 5 meters. If the coordinates represent meters, write a compound inequality that describes the possible x-coordinates for the fence path, solve it, and graph the solution on a number line (describe the graph).
3. A factory produces between 12,500 and 15,800 units per day. Due to a new efficiency initiative, production is expected to increase by at least 2,300 units but no more than 3,700 units. Write a compound inequality that represents the possible daily production after the initiative, then solve for the range of possible production values. What is the minimum number of units the factory could produce after the initiative?

…and 4 more problems

1. Emma is designing a science fair display that needs to be between 120 and 180 square inches in area. The display must be rectangular with a width of exactly 15 inches. Write a compound inequality to represent all possible lengths, in inches, that the display can have.
2. 2(x + 3) - 5 < 7 and 3x - 4 > 2 = ?
3. Aisha is designing a community garden with a rectangular plot that must be at least 15 feet wide but no more than 25 feet wide. The length of the plot must be at least 30 feet longer than the width, but the total area cannot exceed 1,500 square feet. If the width is represented by w and the length by l, which of the following systems of inequalities correctly models the constraints for Aisha's garden plot?

…and 4 more problems

1. Matiu is helping his school's outdoor education program design a new obstacle course. The budget allows for a rope course that must have a total length between 150 and 300 meters. The course will have 3 sections of equal length. Additionally, each section must be at least 30 meters long but no more than 80 meters long to meet safety requirements. Let x represent the length of each section in meters. Write and solve a compound inequality to find all possible lengths for each section that satisfy both the budget and safety requirements.
2. 3x + 7 > 16 and 2x - 5 ≤ 9
3. Liam is organizing a school field day event and needs to set up a volleyball net. The net's height must be at least 220 centimeters but no more than 250 centimeters above the ground to meet official regulations. The net is attached to two poles, and each pole has an adjustable section that can extend the pole's height by x centimeters. The fixed part of each pole is 185 centimeters tall. Write and solve a compound inequality to find all possible extension lengths x (in centimeters) that will keep the net height within the required range.

…and 3 more problems