Seventh Grade · Math · week 23

Graphing inequality solution sets

Graph the solution set of a one-variable inequality on a number line, choosing the correct circle type and shading direction.

An inequality usually has infinitely many solutions, so instead of a single point, its solution graphs as a ray on a number line. Use an OPEN circle for < or > (the boundary number itself is not a solution) and a CLOSED (filled) circle for <= or >= (the boundary number IS a solution).

After placing the circle, shade toward every number that makes the inequality true: shade right for "greater than," left for "less than." If an inequality needs solving first, solve it completely, then graph the final simplified form.

📋 For the teacher
Teach it (10–15 min):
  • Practice reading each symbol in full words out loud: "greater than or equal to," not just "the wiggly one."
  • Use the open-versus-closed rule as a simple test every time: does the boundary number itself count as a solution?
  • If an inequality needs solving first, solve it completely (watching for a possible flip) before drawing anything.
  • Test a sample number against the final graph, the same way you would check an equation's solution.
Talk about it:
  • How do you decide between an open circle and a closed circle?
  • How do you decide which direction to shade?
  • Why must an inequality be fully solved before you can graph it correctly?

Mastery looks like: They solve an inequality if needed, then graph it with the correct circle type and shading direction.

Common stumbles: Using an open circle when the boundary should be included (or the reverse); shading the wrong direction on the number line.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

Number LineCount, add, subtract, and skip-count with animated hops and a friendly voice.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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