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.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Many real situations set a limit rather than an exact amount. A ride requires riders taller than 48 inches; a bag must weigh less than 50 pounds. Sixth graders write these conditions as inequalities of the form x > c or x < c, where c is a number, and they understand that such an inequality has infinitely many solutions, not just one. Every height above 48 inches, including 48.5 and 60.25, satisfies h > 48.
Graphing on a number line shows all those solutions at once. An open circle marks the boundary value when it is not included, and an arrow or shaded ray points in the direction of the solutions. The standard names only strict inequalities, but students commonly meet 'at least' and 'no more than' too, which use ≥ and ≤ with a closed circle. Interpreting the context matters as well: if x counts people, only whole numbers make sense, even though the inequality itself includes fractions.
For x < 3 students sometimes shade to the right. Testing a value (is 5 < 3?) tells them which side holds the solutions.
x > 7 does not include 7, so the circle is open. A closed circle means the boundary is a solution.
Students may say x > 2 has the solutions 3, 4, 5 and so on. Values like 2.1 and 5/2 work too, which is why there are infinitely many.
On a school road, drivers must go slower than 25 miles per hour. Write an inequality for an allowed speed s and describe its graph. Is 24.5 mph allowed?
Answer: s < 25; the graph has an open circle at 25 shaded left; 24.5 mph is allowed.
Match phrases to symbols explicitly: more than, greater than, above and exceeds point one way; less than, below, under and fewer than point the other. Testing one value on each side of the boundary is a reliable habit for choosing the direction.
Typical assessment items show a number line graph and ask for the matching inequality, or describe a constraint and ask for the inequality and graph.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: C) a > 13
Older than 13 means more than 13: a > 13.
Answer: B) x < 4
Shaded left means values less than 4, and the open circle means 4 is not included: x < 4.
Answer: A) 2.51
Only 2.51 lies to the right of 2.5. The value 2.5 itself is not included because the inequality is strict.
Answer: infinitely many (also accepted: infinite, infinity)
Every number less than 10, including fractions, decimals and negatives, is a solution, so there are infinitely many.
Answer: w < 23 (also accepted: w<23, 23 > w)
Less than 23 is written w < 23. The same condition can be written 23 > w.
A full lesson with slides, activities and an exit ticket on writing and graphing inequalities, pitched to grade 6 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 6.EE.B.8 with an answer key, ready in about a minute.
Make a worksheet →Turn writing and graphing inequalities into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Between any two numbers there are always more numbers. Every value on the correct side of the boundary, including fractions and decimals, makes the inequality true.
When the boundary value is not a solution, as with > and <. A closed circle is used for ≥ and ≤.