Linear Inequalities Worksheet with Answers

Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

Algebra 1 Math Worksheets – Mathbot, the Math Made Easy robot coach, with free printable worksheets for Algebra 1

Looking for a linear inequalities worksheet with answers PDF? Then this Algebra 1 worksheet on Solving, Graphing and Modeling with Inequalities gives problems ranked from easy to hard. These problems train solving multi-step inequalities, reversing the sign correctly, graphing on a number line and writing interval notation, as required by A-REI.B.3. Early problems use one operation at a time, and later ones combine distribution and variables on both sides.

The last six problems model real constraints (A-CED.A.1 and A-CED.A.3): budgets, averages, profits and temperature ranges. Decide whether the answer must be a whole number.

Standards: A-REI.B.3, A-CED.A.1, A-CED.A.3 · Level: Grade 9 Algebra 1

Problem 1 Add and compare ★★★

Solve x + 7 > 12 and describe the graph.

Problem 2 Divide by a positive ★★★

Solve 3x ≤ 21.

Problem 3 Two steps with a fraction ★★★

Solve x4 − 2 ≥ 1.

Problem 4 Reverse the sign ★★★

Solve −2x < 14.

Problem 5 Write from a graph ★★★

Write the inequality shown by the graph.

Closed circle at −2, shaded left.

Problem 6 Variables on both sides ★★★

Solve 6x − 5 > 2x + 11 and graph the solution.

Problem 7 Negative coefficient ★★★

Solve 7 − 3x ≥ 22.

Problem 8 Distribute first ★★★

Solve 4(x − 2) < 2x + 10.

Problem 9 Fraction inequality ★★★

Solve 2x − 13 ≤ 5.

Problem 10 Compound inequality (and) ★★★

Solve −7 < 2x − 1 ≤ 9, graph it and write it in interval notation.

Problem 11 Compound inequality (or) ★★★

Solve 3x + 2 < −7 or 2x − 5 ≥ 9 and graph the solution.

Problem 12 Read a segment ★★★

Write the compound inequality and the interval notation for the graph.

A shaded segment from −1 to 4.

Problem 13 Interval notation ★★★

Write each in interval notation: (a) x > −1 (b) x ≤ 9 (c) 1 < x ≤ 8.

Problem 14 Test values ★★★

Is x = −3 a solution of 6 − 2x > 11? Is x = −2? Then describe all solutions.

The solutions of 6 − 2x > 11.

Problem 15 Camp activities ★★★

A camp trip costs $18 for the bus plus $7.50 for each activity. Jordan can spend at most $60. Write and solve an inequality, then state the greatest number of activities.

Problem 16 Test average ★★★

Dana scored 78, 85 and 91 on three tests. What must she score on the fourth test to have an average of at least 85?

Problem 17 Food truck profit ★★★

A food truck sells wraps for $6.50 each. Each wrap costs $1.90 to make, and the truck has $420 in daily fixed costs. How many wraps must it sell to earn a profit greater than $300?

Problem 18 Greenhouse range ★★★

A greenhouse must stay between 59°F and 86°F, inclusive. With F = 1.8C + 32, find the allowed temperatures in degrees Celsius.

Problem 19 Robotics budget ★★★

A club has $300. A kit costs $24 and a sensor costs $9. It buys 6 kits. Write and solve an inequality for the number of sensors s it can still buy.

Problem 20 Phone plan comparison ★★★

Plan A costs a flat $35 per month. Plan B costs $15 plus $4 per gigabyte. For how many gigabytes g is Plan B cheaper? Use the graph.

Plan A (orange, flat $35) and Plan B (blue, $15 + $4 per GB).

Linear Inequalities lesson Linear Inequalities test Linear Inequalities quiz