Harder Equations

Harder equations have the pronumeral on both sides, such as \(12x - 4 = 13x + 4\). In NSW Year 8 maths (NESA outcome MA4‑EQU‑C‑01) the first move is to take the smaller pronumeral term away from both sides, which leaves an ordinary one-step or two-step equation.

You will collect like terms first, add a term when it is subtracted, divide by negatives and decimals as in \(1.2x + 3 = 0.2x\), and simplify a side with no pronumeral before you start. You will check answers by working out each side separately, pick out an equation with the same solution, and compare two tanks filling at different rates to find when they hold the same amount. It is part of Year 8 Equations.