6th Grade Inequalities on the Number Line Worksheet (PDF)

6th Grade math worksheet: Inequalities on the Number Line – Maths PDF

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This grade 6 inequalities worksheet for 6th Grade covers inequalities on the number line (Common Core 6.EE.B.5, 6.EE.B.8), with a free PDF to print.

These 20 problems practice inequalities and their graphs (Common Core 6.EE.B.5 and 6.EE.B.8). You will test values, graph x greater or less than a number on a number line, write inequalities from words and graphs, and solve real-world problems about limits and goals.

Grade 6 · Common Core State Standards: 6.EE.B.5, 6.EE.B.8

Grade 6 inequalities worksheet: exercises 1 to 10

Exercise 1 – Is it a solution? (greater than)

Is 6 a solution of $x > 4$?

Exercise 2 – Is it a solution? (at least)

Is 4 a solution of $x \ge 9$?

Exercise 3 – Is it a solution? (expression)

Is 8 a solution of $x + 2 < 10$?

Exercise 4 – Graph x > 3

Number line.

Graph $x > 3$ on a number line.

Exercise 5 – Graph x <= 2

Number line.

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

Exercise 6 – Graph with a negative

Graph $x \ge -1$ on a number line.

Exercise 7 – Write from a graph (open)

A ray starting at 4.

Write an inequality for the graph.

Exercise 8 – Write from a graph (closed)

A ray starting at -2.

Write an inequality for the graph.

Exercise 9 – Less than

Write an inequality for “a number $x$ is less than 7.”

Exercise 10 – At least

Write an inequality for “a number $x$ is at least 12.”

Exercises 11 and up

Exercise 11 – No more than

Write an inequality for “a number $x$ is no more than 20.”

Exercise 12 – More than

Write an inequality for “a number $x$ is more than 15.”

Exercise 13 – List solutions

List three solutions of $x > 5$.

Exercise 14 – Solutions with decimals

List three solutions of $x \ge 2.5$. Is 2.5 a solution?

Exercise 15 – Speed limit

The speed limit on a highway is 65 miles per hour. Write an inequality for the legal speeds s and graph it on a number line from 0 to 80.

Exercise 16 – Elevator

An elevator can carry no more than 1,500 pounds. A group of 12 people weighs 1,380 pounds. Write an inequality for the allowed weight w and decide whether the group can ride.

Exercise 17 – Game points

Number line.

Maya needs at least 8 points to win a game. Write an inequality for the points p that win and graph it.

Exercise 18 – Book budget

Jamal has $25. Each book costs $4. The inequality 4b ≤ 25 shows how many books b he can buy. Test b = 6 and b = 7, then tell the greatest number of books he can buy.

Exercise 19 – Ride height

To ride a roller coaster, a child must be taller than 48 inches. Write an inequality for the height h. Is 48 a solution? Is 48.5?

Exercise 20 – Infinitely many

Explain why the inequality x > 3 has infinitely many solutions.

Exercise 21 – Snow day

A school closes for a snow day when the temperature t is below 32°F. Write an inequality and graph it on a number line from 20 to 40. Is 32 a solution? Is 31.5?

Key facts behind this grade 6 inequalities worksheet

Key facts

An inequality uses <, >, ≤, or ≥ and usually has infinitely many solutions.
Open circle: the number is not included (< or >).
Closed circle: the number is included (≤ or ≥).
Shade right for greater values and left for lesser values.
At least means ≥ and at most or no more than means ≤.

How to use this grade 6 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 grade 6 inequalities worksheet as a PDF with the button below and keep it with your notes.

All Grade 6 chapters: Grade 6 math.

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