Inequalities & Graphing
Graphing Inequalities (x > 5, etc.)
Graphing an inequality on a number line shows all solutions. Use an open circle for > or < (not equal), and a closed circle for ≥ or ≤ (equal included). Shade in the direction of the solutions.
Watch & Learn
Watch a clear, friendly video explanation of Graphing Inequalities (x > 5, etc.):
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Worked Examples
Follow along with these step-by-step examples. Take your time — there's no rush!
Problem
Graph: x > 5
Step-by-Step Solution
Place an open circle at 5 (5 is NOT included because of >).
Shade to the right of 5 (all numbers greater than 5).
Arrow points right toward infinity.
Answer
Open circle at 5, shaded right
Problem
Graph: x ≤ −2
Step-by-Step Solution
Place a closed circle at −2 (−2 IS included because of ≤).
Shade to the left of −2 (all numbers less than or equal to −2).
Arrow points left.
Answer
Closed circle at −2, shaded left
Problem
Graph: x ≥ 0
Step-by-Step Solution
Place a closed circle at 0.
Shade to the right (all numbers ≥ 0).
Answer
Closed circle at 0, shaded right
Problem
Write the inequality shown: open circle at −3, shaded to the right
Step-by-Step Solution
Open circle means the value is NOT included → use > or <.
Shaded right means values greater than −3.
Inequality: x > −3
Answer
x > −3
Problem
Graph: −2 ≤ x < 4 (compound inequality)
Step-by-Step Solution
Closed circle at −2 (included), open circle at 4 (not included).
Shade the region between −2 and 4.
Answer
Closed circle at −2, open circle at 4, shaded between
Your Turn — Practice Problems
Try all 5 problems on your own first. Write out your work — that's how it sticks!
💡 Tip: Don't peek at the answers until you've genuinely tried each one.
Describe the graph of x < 3
Describe the graph of x ≥ −4
What circle type for x > 7?
What circle type for x ≤ 10?
Describe the graph of x < −1
Write the inequality: closed circle at 5, shaded right
Write the inequality: open circle at 0, shaded left
Describe the graph of x > −6
Write the inequality: closed circle at −2, shaded left
Describe the graph of −1 < x ≤ 4
What does an open circle mean on a number line?
What does a closed circle mean on a number line?
Finished all 12? Give yourself a pat on the back — then check your work!
Keep going — you're on a roll!
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