Write and Graph Inequalities

Students write inequalities of the form x > c or x < c to represent real-world constraints, such as a height requirement or a speed limit. They graph the solution set on a number line using open or closed circles and understand that the graph represents all solutions.

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Grade 6 · Equations and Inequalities · question 1 of 3

0 of 20

20 rungs. A star at the top.

Which inequality in x does the graph show?

x > 1

x ≥ 1

x ≤ 1

x < 1

How it is taught

0:00 of 3:26

An inequality compares a variable to a number.

Less than means the variable is smaller.

An open circle shows the endpoint is not included.

Read it: Words, then the sign, then the ray

"x is at least 3" lets x be 3 or any number greater than 3, so the sign is ≥: x ≥ 3. On the line it is a filled circle at 3 and a ray to the right.

Read the words and ask: does the number itself count?
Write the sign: ≥ or ≤ when the number counts, > or < when it does not.
Graph it: a filled circle if the number counts, an open one if not, then the ray toward the greater or the lesser numbers.

At least, at most and no more than all include the number, so their signs carry the line underneath: ≥ and ≤.

Greater than and less than leave the number out: > and <, with an open circle.

On the line greater numbers are to the right and lesser numbers to the left, below 0 too.

The circle says whether the number counts; the ray says which side holds the rest.

Writing x > 3 for "x is at least 3".

At least includes 3 itself: x ≥ 3, with a filled circle at 3.

Write "w is at least 15" as an inequality. — w ≥ 15. At least includes 15 itself, so the sign is ≥: w ≥ 15.

h > 48 (taller than 48 inches)

Imagine a sign at the roller coaster: 'You must be taller than forty-eight inches to ride.' Let's turn that into math.

First, we pick a variable. Let h stand for your height, in inches.

The words 'taller than' mean greater than. In math, that's the sign that points to the right.

So our inequality is: h is greater than forty-eight.

Now we'll graph it. We draw a number line with forty-eight in the middle.

We put a circle right on forty-eight, because that's the boundary.

But we leave the circle OPEN — empty inside — because forty-eight itself is NOT a solution. You have to be taller than that.

Then we shade everything to the right, because every number bigger than forty-eight works.

Let's check one. Is fifty greater than forty-eight? Yes! So a height of fifty inches is a solution.

Grade 6 · Roller coaster height rule

Our inequality is h greater than forty-eight, and the graph shows every height that lets you ride. Great job!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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