Circle + arrow
Read the circle (open/closed) for the symbol type and the arrow for the direction.
Why it works
Filled dot = “and this one too”.
Inequalities · Meet inequalities · 1.3
Graph on a number line.
An inequality’s solutions form a ray on the number line. A closed (filled) circle marks an included boundary (≤, ≥); an open circle marks an excluded one (<, >). The arrow shades every value that works.
See it work.
Watch the method
Graph on a number line
Closed circle = included (≤/≥); open = excluded (</>); arrow shows direction.
1
Read the graph
A closed circle includes the value (≤/≥); an open circle excludes it. The arrow shows the direction.
On the number line
Shade the solutions.
A open circle excludes 4; the arrow points to every value that works.
Practice until it feels automatic.
Your turn
Solve for x.
Type the solution, e.g. x < 4 (you can write <= for ≤).
streak 0
best 0
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The idea underneath.
From easy to tricky.
A number line has a closed circle at -1 and the arrow points right. Write the inequality.
1
Read the graph
A closed circle includes the value (≤/≥); an open circle excludes it. The arrow shows the direction. x ≥ -1
A number line has an open circle at -4 and the arrow points left. Write the inequality.
1
Read the graph
A closed circle includes the value (≤/≥); an open circle excludes it. The arrow shows the direction. x < -4
A number line has an open circle at -5 and the arrow points right. Write the inequality.
1
Read the graph
A closed circle includes the value (≤/≥); an open circle excludes it. The arrow shows the direction. x > -5
Where students slip.
Trap
Filling a circle for < or >.
Fix
Strict inequalities use an OPEN circle.
Trap
Shading the wrong way.
Fix
x > n shades to the right; x < n to the left.
Test yourself.
The Test
12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.
0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so
t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).Core
Core (4)
C1
A number line has an open circle at 1 and the arrow points right. Write the inequality.
Need a hint?
- Closed circle → ≤ or ≥.
- Arrow right → >; arrow left → <.
C2
A number line has an open circle at 6 and the arrow points left. Write the inequality.
Need a hint?
- Closed circle → ≤ or ≥.
- Arrow right → >; arrow left → <.
C3
A number line has a closed circle at 6 and the arrow points right. Write the inequality.
Need a hint?
- Closed circle → ≤ or ≥.
- Arrow right → >; arrow left → <.
C4
A number line has an open circle at 3 and the arrow points left. Write the inequality.
Need a hint?
- Closed circle → ≤ or ≥.
- Arrow right → >; arrow left → <.
Apply
Apply (4)
A1
A number line has a closed circle at 4 and the arrow points right. Write the inequality.
Need a hint?
- Closed circle → ≤ or ≥.
- Arrow right → >; arrow left → <.
A2
A number line has a closed circle at -5 and the arrow points right. Write the inequality.
Need a hint?
- Closed circle → ≤ or ≥.
- Arrow right → >; arrow left → <.
A3
A number line has a closed circle at -5 and the arrow points right. Write the inequality.
Need a hint?
- Closed circle → ≤ or ≥.
- Arrow right → >; arrow left → <.
A4
A number line has a closed circle at -5 and the arrow points right. Write the inequality.
Need a hint?
- Closed circle → ≤ or ≥.
- Arrow right → >; arrow left → <.
Extension
Extension (4)
E1
A number line has a closed circle at 2 and the arrow points right. Write the inequality.
Need a hint?
- Closed circle → ≤ or ≥.
- Arrow right → >; arrow left → <.
E2
A number line has an open circle at 1 and the arrow points left. Write the inequality.
Need a hint?
- Closed circle → ≤ or ≥.
- Arrow right → >; arrow left → <.
E3
A number line has an open circle at 1 and the arrow points right. Write the inequality.
Need a hint?
- Closed circle → ≤ or ≥.
- Arrow right → >; arrow left → <.
E4
A number line has a closed circle at -4 and the arrow points right. Write the inequality.
Need a hint?
- Closed circle → ≤ or ≥.
- Arrow right → >; arrow left → <.