Linear Inequalities Worksheets Grade 9

1. A line segment on a coordinate plane has endpoints at (2x + 7, 0) and (0, x - 2). The midpoint of this segment lies to the right of the y-axis and below the x-axis. Write an inequality to represent all possible values of x that satisfy these conditions.
2. Emma is a graphic designer who needs to print custom posters. The printing company charges a flat setup fee of $35, plus $3 per poster. Emma's client has a budget of at most $215 for the printing. If x represents the number of posters printed, write and solve a linear inequality to determine the maximum number of posters Emma can print without exceeding the budget. Graph the solution on a number line.
3. 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.

…and 4 more problems

1. A tech company is analyzing their monthly revenue. Their basic subscription brings in $800 per month, and they earn an additional $12 for each premium user. The company needs their total monthly revenue to be at least $5000 to cover operating costs. If p represents the number of premium users, write and solve an inequality to determine the minimum number of premium users needed to meet this revenue requirement.
2. Noah is managing a school fundraiser where he sells custom T-shirts. The fixed cost to set up the printing equipment is $150, and each T-shirt costs $7 to produce. Noah plans to sell each T-shirt for $15. If he wants to make a profit of at least $250, how many T-shirts must he sell? Write and solve an inequality to represent this situation, where x is the number of T-shirts sold.
3. Tane is managing a community garden. He has 117 meters of fencing to enclose a rectangular plot where the length must be at least 9 meters more than three times the width. If the perimeter must use all the fencing, write and solve an inequality to find the possible widths of the garden that satisfy both conditions. Graph the solution on a number line.

…and 4 more problems

1. 5(3x - 7) - 9 > 2(5x + 1) + 11
2. 4(3x - 11) - 7(x + 5) ≥ 2(6x - 13) + 9
3. A right triangle is positioned on a coordinate plane with vertices at (0,0), (x,0), and (0,2x-4). The area of the triangle is greater than 16 square units. Write an inequality that represents all possible values of x, assuming x > 2.

…and 6 more problems