Solving equations with variables on both sides

Collect variable terms on one side and constants on the other, then solve each equation by undoing operations in reverse order.

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Te reo Māori terms

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Learning objective overview

Master Teaching Guide coverage for this objective.

Resources

  • Alpha textbook: Equations with x on both sides, Ex 14.07, pg 224 and
  • Alpha textbook: PSE 14B, pg 224
  • Alpha textbook: Variables and numbers on both sides, Ex 14.11, pg 232
  • Alpha textbook: and PSE 14D, pg 232
  • Other: PSE IAR no 99A
  • Other: Variables and numbers on both sides, Ex 14.11, pg 232
  • Other: and PSE 14D, pg 232
  • CorbettMaths worksheetQuestions PDF · Answers
  • Beta: Skills in Chapters 10, pg 178-185
  • Beta: Chapter 10 – pgs 176 to 197
  • Beta: Contextual questions: Ex 10.06, Ex 10.08, Ex 10.12, and Ex 10.14

Terminology

  • equation
  • solution
  • inverse operation
  • inverse
  • isolate
  • variable
  • coefficient
  • like terms
  • collect
  • both sides

Task goals

  • Identify and collect like terms with variables on both sides, such as $3x$ and $2x$, to simplify the equation.
  • Move constant terms to one side and variable terms to the other by applying inverse operations to both sides.
  • Solve equations of the form $ax + b = cx + d$ by collecting terms and undoing operations in reverse order.
  • Verify solutions by substituting back into the original equation to check balance.

Key skills

  • Solve equations
  • Variables both sides
  • One step equations
  • Two step equations

Quick stats

  • 81 total questions
  • 3 difficulty levels
  • Answers included