Linear Inequalities Worksheets Grade 8

1. Is (4, 8) a solution to y ≥ 2x + 2?
2. Noah is planning a community garden and needs to buy soil and fertilizer. He has a budget of $200. Soil costs $4 per bag and fertilizer costs $8 per container. Noah needs at least 25 bags of soil for the garden beds. Write an inequality that represents all possible combinations of soil bags (s) and fertilizer containers (f) that Noah can purchase while staying within his budget and meeting the minimum soil requirement.
3. Is (9, 13) a solution to y ≥ 4x - 23?

…and 4 more problems

1. Is (11, 9) a solution to y ≤ 2x - 13?
2. A company is manufacturing two types of solar panels. Model X requires 3 hours of assembly time and 2 hours of testing time. Model Y requires 4 hours of assembly time and 1 hour of testing time. The factory has at most 240 hours of assembly time available per week and at most 100 hours of testing time available per week. If x represents the number of Model X panels and y represents the number of Model Y panels produced per week, which system of inequalities represents these constraints?
3. Maya is planning a community garden and needs to buy fencing for two rectangular plots. The first plot requires at least 3 times as much fencing as the second plot. The total amount of fencing available is 120 feet. If x represents the fencing for the first plot and y represents the fencing for the second plot, which system of inequalities represents this situation?

…and 3 more problems

1. Isabella is helping her grandmother create two types of gift baskets for a charity auction. Each small basket requires 2 apples and costs $3 to make. Each large basket requires 7 apples and costs $12 to make. Isabella's grandmother has 77 apples available and a budget of $132. Write a system of inequalities that represents the number of small baskets (x) and large baskets (y) they can make, given the constraints. Then, determine if they can make 12 small baskets and 7 large baskets.
2. Maya is planning a community garden and needs to buy fencing for two rectangular plots. The first plot requires fencing that costs $4 per foot, and the second plot requires fencing that costs $6 per foot. She has a budget of $300 for fencing and needs at least 20 feet of the $6-per-foot fencing for the vegetable plot. Write an inequality that represents all possible combinations of fencing lengths (x for the $4-per-foot fencing, y for the $6-per-foot fencing) that Maya can purchase while staying within her budget and meeting the vegetable plot requirement.
3. Kaia is organizing a school cultural festival and needs to buy two types of traditional fabric for decorations. She has a budget of $240. Fabric type A costs $9 per meter, and fabric type B costs $12 per meter. Kaia needs at least 12 meters of fabric type B for the main stage backdrop. She also wants to buy at least 3 times as many meters of fabric type A as fabric type B. Write a system of inequalities that represents Kaia's constraints, where x represents the meters of fabric type A and y represents the meters of fabric type B. Then, test whether Kaia can buy 30 meters of fabric type A and 10 meters of fabric type B while meeting all her requirements.

…and 2 more problems