Inequalities — Practice Companion

Eight questions, building from straightforward to exam-style. Each comes with a four-tier support ladder — use it in order, and only as far as you need:

🤔 Socratic prompt asks you a question to get you thinking · 💡 Hint gives you a piece of method · ✅ Check my answer tells you if you're right and nudges you if not · 👀 Worked solution is the last resort, and unlocks once you've genuinely tried. Two habits to carry through: pause at every negative divide, and for quadratics, sketch the parabola and read the region.

💛 Before you finish — a reflection

Look back over the eight questions and notice, without judgement:

On the sign-flip questions, did you catch the flip as you divided, or only when checking? Building the pause-at-every-negative-divide habit is worth more than speed.
For the quadratics, did sketching the parabola make "outside the roots" versus "between the roots" feel obvious rather than memorised? If so, trust the picture — it rebuilds itself when a rule won't.
Which rung of the ladder actually unstuck you when you needed it? Knowing whether a question, a hint, or checking-and-revising helps you most is a tool for every topic to come.

That last noticing matters more than any score.