Solving equations with variables on both sides

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)

NA5-7
NA6-5

New NZC (2026)

NZC26-P4-ALG-ER-P-Y10-02

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.

Where this fits

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

Before

Merit-Level Algebraic Methods: Multi-Step Worked Problems

AS91027 Mixed Algebraic Procedures Practice (Achievement)

AS91027 Exam-Style Algebra Review (Mixed Practice Exam)

You are here

Solving equations with variables on both sides

Forming and solving linear equations and linear inequalities with rational number coefficients (e.g. −2/5 x + 5 ≤ −10), giving exact or rounded solutions, and representing the solution on a number line

Statement▸

Year 10 · Algebra · Equations and relationships

NZC26-P4-ALG-ER-P-Y10-02