L4 · Inequalities clinic (interpret only)

Learning goal

“I can move between all three faces of an inequality - symbols, number-line model, and real situation - and I can verify any claim about solutions by substitution. I interpret inequalities; I do not solve them (that is Grade 9).”

Solution set — the collection of ALL values that make an inequality true; on the number line it is the whole shaded ray, not a list.

Interpret — read off what an inequality says (its type, its model, its solutions, its situation) without changing it into a solved form.

Worked example

Take the situation "A ferry takes at most 60 cars." Face 1 (symbols): c = number of cars; "at most" includes the boundary -> c ≤ 60. Face 2 (model): closed dot at 60, shading left (all counts from 0 up to 60 in context). Face 3 (solutions): 60 is a solution (60 ≤ 60); 61 is not (61 ≤ 60); 45 is (45 ≤ 60). Say it plainly: symbols, model and situation are three writings of one fact - fluency is converting in ANY direction, not just words -> symbols.

Check yourself — explain it

The model of c ≤ 60 has a closed dot because...

Paired problem — example still visible

A ray has an open dot at 10, shading right. Write the inequality and invent a matching situation. -> x > 10; e.g. "Entry is for children over 10" or "The temperature rose above 10 °C" - any strict "more than 10" situation.

Faded completion — last step is yours

"Situation: 'A tank must hold more than 500 L to start the pump.' Symbols: V ______ 500 (V in litres). Model: ______ dot at 500, shading ______." -> >; open; right

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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