Solving inequalities

Solve one-step and two-step linear inequalities, including those requiring expanding brackets, and correctly reverse the inequality sign when multiplying or dividing by a negative number, applying this to real-world word problems.

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Te reo Māori terms

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • NA6-5
New NZC (2026)
  • NZC26-P4-ALG-ER-K-Y9-03
  • NZC26-P4-ALG-ER-K-Y10-07
  • NZC26-P4-ALG-ER-P-Y9-03
  • NZC26-P3-ALG-ER-P-Y7-02
  • NZC26-P3-ALG-ER-P-Y8-02

Resources

Terminology

  • inequality
  • inequality sign
  • greater than
  • less than
  • greater than or equal to
  • less than or equal to
  • number line

Task goals

  • Solve a one-step inequality involving addition, subtraction, multiplication, or division by a positive number.
  • Solve a two-step inequality that combines multiplication or division with addition or subtraction.
  • Solve a two-step inequality that requires dividing by a negative number, correctly reversing the inequality sign.
  • Solve an inequality that requires expanding brackets or combining like terms on one or both sides before isolating the variable, reversing the sign whenever dividing by a negative.
  • Solve an inequality in which the entire expression is written as a single fraction, isolating the variable across multiple steps.
  • Write an inequation to model a real-world situation involving a fixed fee plus a per-unit cost, or a maximum/minimum condition, then solve it to answer the question.

Where this fits

What leads into this objective, and where it goes next.

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Solving inequalities

Solving inequalities

Know

Multiplying or dividing by a negative number reverses an inequality.

Statement▸
Year 9 · Algebra · Equations and relationships
NZC26-P4-ALG-ER-K-Y9-03
Do

Multiplying or dividing by −1 in inequalities (e.g. −3 < 5)

Statement▸
Year 9 · Algebra · Equations and relationships
NZC26-P4-ALG-ER-P-Y9-03

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