Reach for the Star

Inequalities and number lines · Optional extension

L022 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.

Stretch

Solve 3−2x<11 and show the solution in words.

Reveal a worked check after attempting

−2x<8, so x>−4; all numbers greater than −4.

Deep challenge

Why does dividing −3x≥12 by −3 reverse the sign? Give a numerical check.

Reveal a worked check after attempting

x≤−4; multiplying an inequality by a negative reverses order, e.g. −3×−4=12 and x=−5 gives 15≥12.

Recall & Review: feedback and extension integration

Lesson L022: Inequalities and number lines

Objective: Solve linear inequalities and represent solution sets on number lines. Explain endpoint inclusion and order reversal.

60-minute structure: 0-7 Connect & Check; 7-14 Share; 14-25 Present/model; 25-44 Apply route choice/practice; 44-52 independent exam-style check; 52-60 Recall & Review, WWW/EBI and next step.

What Went Well (WWW)

I represented the algebraic structure accurately, kept each transformation valid and checked the result by substitution, graph or equivalent reasoning.

Even Better If (EBI)

I will show the missing inverse operation or algebraic step, keep signs and brackets accurate and test the result in the original relationship.

Stretch and deep challenge

Stretch: Solve 3−2x<11 and show the solution in words.

Deep challenge: Why does dividing −3x≥12 by −3 reverse the sign? Give a numerical check.