Worked example 1
Write an inequality: “You must be at least 13 years old.”
“At least 13” means 13 or more, so a ≥ 13, where a is age.
Answer: a ≥ 13
Grade 6 Math · Topic 50
Writing and Graphing Inequalities
An inequality compares two values using <, >, ≤, or ≥. Inequalities have many solutions, so we graph them on a number line: an open circle for < or > (boundary not included) and a closed circle for ≤ or ≥ (boundary included).
Lesson alignment: 6.EE.B.8 · Take your time. You can return to this lesson whenever you need it.
Explore visually
Graph an inequality on a number line
Choose a boundary and inequality sign. The ray shows every value that makes the inequality true.
Think first: Which direction should include the values that make this inequality true?
Ready? Reveal the model and try your prediction
Swipe horizontally to see the full diagram.
Turn on JavaScript to adjust this model. The examples and practice below work without it.
Follow the worked examples
Read each step, then cover the explanation and see if you can explain why it works.
Worked example 2
Describe the graph of x > 4.
Open circle at 4 (since 4 itself is not a solution), shaded to the right (greater values).
Answer: Open circle at 4; shade right.
Try a few on your own
Work these on paper first. Open “Check” when you are ready to compare your answer.
- x is more than 5
Check
x>5
- y is at most 10
Check
y≤ 10
- a is at least 0
Check
a≥ 0
- n is less than or equal to -3
Check
n≤ -3
- p is no more than 25
Check
p≤ 25
- k is greater than -6
Check
k>-6
- The score must be at least 80
Check
s≥ 80
- The bag holds fewer than 12 items
Check
b<12
Try this situation 1
To ride a roller coaster, you must be at least 48 inches tall. Write an inequality for height h.
Show a worked solution
Answer: h ≥ 48.
“At least” includes 48, so ≥.
Try this situation 2
A backpack can carry no more than 20 pounds. Write an inequality for its weight w.
Show a worked solution
Answer: w ≤ 20.
“No more than” means less than or equal to.
Fresh questions · saved on this device
Practice this skill
Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.
Question 1 of 50 correct so far
Session complete
Check what you learned
Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.
Practice and finish
Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.
Your checkmark, skill-practice sessions, and best exit-check score are saved on this browser and device. The course page can download a progress report to share with a tutor or teacher.
More Grade 6 resources
Use these free materials if you want another explanation, extra paper practice, or a broader review.