Algebra 1 Linear Inequalities in One Variable Worksheet (PDF)

Algebra 1 math worksheet: Linear Inequalities in One Variable – Maths PDF

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This linear inequalities worksheet for Algebra 1 covers linear inequalities in one variable (Common Core A-REI.B.3, A-CED.A.1), with a free PDF to print.

These 20 problems practice linear inequalities (Common Core A-REI.B.3 and A-CED.A.1). You will solve and graph one-variable inequalities, reverse the symbol when needed, work with and/or compounds, and model situations with at least and at most. The first problems are short skill checks, and the last six are word problems that need several steps. Work in order and show every line of your work, because a bare answer earns little credit on a test.

Algebra 1 · Common Core State Standards: A-REI.B.3, A-CED.A.1

Linear inequalities worksheet: exercises 1 to 10

Exercise 1 – Graph x greater than 3

Graph $x > 3$ on a number line.

Exercise 2 – Graph with a closed circle

Graph $x \le -2$ on a number line.

Exercise 3 – Write from a graph

Graph of an inequality.

Write the inequality shown on the number line.

Exercise 4 – Add and compare

Solve $x + 5 < 12$.

Exercise 5 – Subtract on both sides

Solve $x – 4 \ge -1$.

Exercise 6 – Divide by a positive

Solve $3x > 18$.

Exercise 7 – Divide by a negative

Solve $-2x \le 10$.

Exercise 8 – Divide by a negative fraction form

Solve $\frac{x}{-3} < 4$.

Exercise 9 – Two-step

Solve $2x – 5 \ge 9$.

Exercise 10 – Two-step with a negative

Solve $-3x + 4 > 19$.

Exercises 11 and up

Exercise 11 – Variables on both sides

Solve $5x + 2 \le 3x + 12$.

Exercise 12 – Distribute

Solve $4(x – 2) < 2x + 6$.

Exercise 13 – Fraction coefficient

Solve $\frac{2}{3}x – 1 \ge 5$.

Exercise 14 – And compound

Solve $-5 \le 3x – 2 < 7$ and graph the solution.

Exercise 15 – Or compound

Solve $x – 3 < -5 \text{ or } 2x \ge 8$ and graph the solution.

Exercise 16 – Smoothies

Smoothie costs.

Priya has $60. Each smoothie costs $4.50. Write and solve an inequality for the number of smoothies $s$ she can buy. What is the greatest whole number?

Exercise 17 – Saving for a bike

Noah has $44 and earns $12 for each lawn he mows. He wants at least $200 for a bike. Write and solve an inequality for the number of lawns $n$, then find the least whole number.

Exercise 18 – Elevator limit

Total weight with Jamal.

An elevator holds at most 1,000 pounds. Jamal weighs 180 pounds and carries boxes that weigh 45 pounds each. Write and solve an inequality for the number of boxes $b$, then find the greatest whole number.

Exercise 19 – Phone plans

At 150 texts the plans cost the same.

Plan A costs $30 plus $0.10 per text. Plan B is a flat $45. Write and solve an inequality to find the number of texts $t$ for which Plan A costs less than Plan B.

Exercise 20 – Average score

Liam scored 82, 90, and 78 on his first three tests. He wants an average of at least 85 after the fourth test. Write and solve an inequality for the fourth score $x$.

Exercise 21 – Cooler temperature

Safe range: 34°F to 40°F.

Food stays safe in a cooler while its temperature is between 34°F and 40°F, inclusive. The cooler starts at 34°F and warms 1.5°F each hour. Write and solve a compound inequality for the hours $h$ the food stays safe.

Key facts behind this linear inequalities worksheet

Key facts

Use an open circle for < and >, and a closed circle for ≤ and ≥.
Adding or subtracting the same number never changes the inequality symbol.
Multiplying or dividing both sides by a negative number reverses the symbol.
An and inequality is true between endpoints; an or inequality is true on two rays.
“At least” means ≥ and “at most” means ≤.

How to use this linear inequalities worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the linear inequalities worksheet as a PDF with the button below and keep it with your notes.

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