6.EE.8: Write and Graph Inequalities
Also written as 6.EE.B.8 and CCSS.MATH.CONTENT.6.EE.B.8 · Cluster: Reason about and solve one-variable equations and inequalities.
The Official Wording
Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
Common Core State Standards, Grade 6, Expressions & Equations · Read it at the source · Checked October 14, 2026
What 6.EE.8 Means in Plain English
Sixth graders turn a condition into an inequality: “you must be over 48 inches to ride” becomes h > 48. Then they graph it, an open circle at 48 and an arrow to the right, because 48.5, 49 and 60 all work. The solutions never run out.
An inequality has infinitely many solutions where an equation (6.EE.7) had one, and the number line is how students see that. Only x > c and x < c appear here. Two-step inequalities like 3x + 2 > 11 wait for 7th grade (7.EE.4).
6.EE.8 I Can Statements
- I can write x > c or x < c for a real condition.
- I can explain why x > 5 has infinitely many solutions.
- I can graph an inequality with an open circle and an arrow.
6.EE.8 Worked Example
A speed limit as an inequality, graphed, with the one number that does not count sitting right at the circle.
A school-zone sign says speeds must be under 30 miles per hour. Write an inequality for the legal speeds and show the solutions on a number line.
- Choose a variable for the quantity that varies: the speed.Let s = the speed in miles per hour
- “Under 30” means less than 30, not equal to it. 30 itself is not legal.s < 30
- Name a few solutions to feel the set: 25 works, 29 works, 29.9 works. There is no biggest legal speed below 30 and no end to the list.25, 29, 29.9, 29.99 and 12.5 all make s < 30 true
- Graph it: an open circle at 30 because 30 is excluded, then shade to the left with an arrow off the end for every smaller value.Open circle at 30, arrow pointing left
Check it: Pick a point on the arrow and one off it: 20 < 30 is true, 35 < 30 is false. The circle is open because 30 < 30 is false too.
Common Mistakes with 6.EE.8
Listing a few solutions as the answer
x > 5: “the solutions are 6, 7, 8, 9, 10”
Try this: Ask about 5.5 and 100. Both work, so the solution set is every number greater than 5, which the arrow shows.
Filling in the circle
x > 5 graphed with a solid dot at 5
Try this: Test the boundary itself: is 5 > 5 true? No, so the circle stays open to show 5 is not included.
Pointing the arrow the wrong way
“More than 12 people” written as p < 12 and shaded left
Try this: Plug in a number from the shaded side: 3 people is not more than 12, so flip to p > 12 and shade right.
Where 6.EE.8 Fits
Practice 6.EE.8
Quick Check
- Write an inequality for “the temperature stayed below 40 degrees.”
- Name three solutions of x > 7 that are not whole numbers.
- How is x < 3 graphed on a number line?