Linear Inequalities Worksheets Grade 9

1. A right triangle is positioned on a coordinate plane with vertices at (0,0), (x,0), and (0,2x-4). The area of this triangle is greater than 12 square units. Write an inequality that represents all possible values of x, assuming x > 2.
2. 3(2x - 7) + 5 ≥ 2(4x - 3) - 9
3. Charlotte is a project manager at a construction firm. She is ordering steel beams for a new building. The supplier charges a flat delivery fee of $85, plus $12 for each steel beam ordered. Charlotte's budget for this order is at most $1,525. If x represents the number of steel beams she orders, write and solve an inequality to find the maximum number of steel beams Charlotte can order without exceeding her budget.

…and 5 more problems

1. 3(2x - 5) + 7 < 4x + 13
2. A tech startup is analyzing their server capacity needs. Their current user base grows at a rate where the number of users U(t) = 500 + 75t, where t is months from now. Their server capacity C can handle up to 2000 users simultaneously. The company wants to know when they'll need to upgrade their servers. Write an inequality that represents when the user base will exceed server capacity, then solve for t.
3. Olivia is organizing a community art fair and needs to rent tables and chairs. Each table costs $15 to rent, and each chair costs $3 to rent. The venue requires that the number of chairs be at least three times the number of tables for proper seating. Olivia's total budget for renting tables and chairs is at most $189. Let t represent the number of tables. Write and solve a linear inequality to determine the maximum number of tables Olivia can rent.

…and 3 more problems

1. A tech startup is analyzing their monthly server costs. Their basic hosting fee is $150 per month, plus $0.05 per gigabyte of data transferred. The company's budget for server costs cannot exceed $500 this month. Write and solve an inequality to determine the maximum gigabytes of data they can transfer while staying within budget.
2. 3(2x - 5) + 7 < 4x - 2
3. Noah is planning a fundraising event for his school's robotics club. He needs to rent a venue that costs a base fee of $150, plus $12 per attendee for catering. The club's total budget for the event cannot exceed $750. If x represents the number of attendees, write and solve an inequality to find the maximum number of attendees Noah can have while staying within the budget.

…and 4 more problems