Inequalities on a Number Line
📋 What it is
Inequalities (<, >, ≤, ≥) show a RANGE of answers; flip the sign when you multiply/divide by a negative.
🗣️ Coach says
An equation has one answer; an inequality has a whole range. x > 3 means "any number past 3". The one rule that trips people: if you multiply or divide both sides by a NEGATIVE, the sign flips direction.
🧠 Memory hook
Multiply/divide by a NEGATIVE → FLIP the sign. Open circle = not included, filled = included.
😂 Giggle
What do you call two friends who love algebra?
Algebros!
😲 Whoa!
Speed limits, age ratings and "you must be THIS tall" signs are all inequalities you obey every day without writing them.
✅ Quick check: You divide both sides of −2x < 6 by −2. What happens to the sign?
Say your answer out loud first — then reveal.
It flips: x > −3.
Dividing or multiplying an inequality by a negative reverses its direction.
🪄 Trick question: Does x < 5 have one answer or many?
Careful — think it through, then reveal.
Many — every number less than 5 works.
Inequalities describe a range of solutions, not a single value.
🧪 Try it! (2 minutes)
Draw a number line and shade "x ≥ 2" with a filled dot. Then shade "x > 2" with an open dot — spot the difference.