Equations — NSW Year 8 Maths
Finding the unknown that makes both sides equal, from comparing phone plans to timing a falling stone. Seven subtopics and 140 practice questions, each with a fully worked solution, aligned to NESA outcome MA4-EQU-C-01.
Equations in NSW Year 8
An equation says that two amounts are equal, such as \(3x + 5 = 20\), and solving it means finding the value of the pronumeral that makes it true. Year 7 introduced one-step and two-step equations with mostly whole numbers. In Year 8, students handle negative, decimal and fraction answers, brackets, fractions on both sides and the pronumeral on both sides, and meet their first equations with a squared pronumeral, such as \(x^2 = 49\).
The seven subtopics below start with one-step and two-step equations, add brackets and fractions, then clear the pronumeral from one side in Harder Equations. Equation Problems turns worded situations into equations, and Simple Quadratic Equations finishes the topic. Equations is one of the 14 topics in NSW Year 8 Maths and belongs to the Number and Algebra strand (NESA outcome MA4‑EQU‑C‑01). These skills are needed to rearrange area and volume formulas, for Graphing Linear Equations later in the year and for the longer equations of Stage 5.
Subtopics
Equations: common questions
What equations do you solve in Year 8 maths?
Linear equations of one or two steps, including ones with brackets, fractions, decimals and the pronumeral on both sides, plus simple quadratic equations such as \(x^2 = 36\) or \(3x^2 = 75\). Every answer can be checked by substituting it back in.
How do you solve an equation with the pronumeral on both sides?
Take the smaller pronumeral term away from both sides, then solve what is left. For \(5x + 3 = 2x + 18\), subtract \(2x\) to get \(3x + 3 = 18\), then \(3x = 15\), so \(x = 5\).
Why do some quadratic equations have two answers?
Both \(5^2\) and \((-5)^2\) equal 25, so \(x^2 = 25\) gives \(x = 5\) or \(x = -5\), written \(x = \pm 5\). An equation such as \(x^2 = -4\) has no solution, because no number squared is negative.
Which NESA outcome covers equations?
Equations sit in Stage 4 of the NSW Mathematics K–10 Syllabus (2022) under outcome MA4‑EQU‑C‑01, which takes in linear equations solved in one or two steps and simple quadratics like \(ax^2 = c\). Year 7 starts this work and Year 8 completes it.
What comes after equations in Year 8?
Equations are used throughout the rest of Year 8, for example to find a missing side from an area or volume formula, and to find where two lines meet in Graphing Linear Equations. In Stage 5 students solve equations with more steps, including ones with an algebraic fraction.