Create Inequalities Worksheets Grade 9

1. Aroha is designing a rectangular garden with a path around it. The garden itself is 7 meters longer than it is wide. A uniform path of width 3 meters surrounds the garden. The total area of the garden plus the path must be no more than 525 square meters. If the width of the garden is represented by w meters, write an inequality in terms of w that represents this constraint.
2. Hana is constructing a rectangular prism with a square base to hold a collection of spherical beads. Each bead has a radius of 1.5 cm and she wants to fit at least 30 beads inside the prism without stacking them (each bead occupies a distinct position). The height of the prism is fixed at 18 cm. The side length of the square base is represented by x cm. Write an inequality in terms of x that represents the condition that the prism must be large enough to contain at least 30 beads, given that each bead requires a cubic space of side length equal to its diameter to sit without touching others.
3. 2x² - 7x + 3 > 0

…and 4 more problems

1. Liam is designing a rectangular garden with a perimeter of 40 meters. He wants the length of the garden to be at least 5 meters more than twice the width. Write an inequality in terms of the width w that represents this situation, then determine the possible range of widths for Liam's garden.
2. Aisha is designing a rectangular banner for a school event. The banner's length must be at least 3 meters more than twice its width. If the area of the banner must be greater than 54 square meters, and the width is represented by w meters, write and solve an inequality to determine all possible widths for Aisha's banner.
3. 2x² - 8x + 6 < 0

…and 4 more problems

1. Aisha is designing a rectangular banner for a school event. The banner must have a perimeter of at most 36 feet. She wants the length to be at least 3 feet more than twice the width. If w represents the width of the banner in feet, write and solve an inequality to determine all possible values for w that satisfy Aisha's design requirements.
2. Liam is designing a rectangular garden with a perimeter of 60 meters. He wants the length of the garden to be at least 5 meters more than twice the width. Write an inequality that represents all possible widths (in meters) that satisfy Liam's design requirements.
3. Lily is planning a school fundraiser and needs to raise at least $408. Each raffle ticket sells for $6. Write an inequality to represent how many tickets Lily must sell to meet the goal.

…and 4 more problems