The goal is to get the unknown variable alone by undoing operations in reverse order using balance principles. Whatever you do to one side must be done to the other to maintain equality.
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foundation maths · algebra & patterns · solving linear equationsdrag it · it is yours
the one idea
why this one carries the topic.
Every rule here is one steady relationship: change one thing by a step, the other moves by the same step, every time. Formula, sequence, equation, line — four ways of writing that relationship.
Solving linear equations requires performing inverse operations in reverse order on both sides to isolate the variable while maintaining the equality balance.
what examiners catch — Students commonly fail when they only apply operations to one side, or when they incorrectly handle negative coefficients by forgetting to flip signs when dividing by negatives.
what you leave with
three things, not forty.
Undo the operations in the reverse of the order they were applied to x: for ax + b = c, subtract b then divide by a; for (x + b)/a = c, multiply by a first
Check your solution by substituting back into the original equation
Do the same inverse operation to both sides at every step so the equation stays balanced
what's underneath
nothing here is a standalone fact.
knowhere maps every concept to what it rests on and what rests on it — 1 underneath this one, 4 built on top. Each one says why, in a sentence, not as an arrow on a diagram.
this conceptsolving linear equationsSolving linear equations requires performing inverse operations in reverse order on both sides to isolate the variable while maintaining the equality balance.
sits under itsubstitution into formulasbecause solving is substitution run backwards
built on itusing formulasbecause Rearranging and break-even both undo operations on both sides of an equation.
built on itsimultaneous equations and the break-even pointbecause a pair is still solved one equation at a time — rearranging comes first
built on itgst and the price you paybecause Removing GST undoes ×1.1, the same inverse step as solving 1.1x = 110.
the rest of algebra & patterns
5 more, same treatment.
Each one is its own knowscape in the app — built for how a particular student takes things in, not one explanation handed to everybody.
patterns and linear relationshipsin the appgraphs and models of practical situationsin the applinear sequencesin the appusing formulasin the appsubstitution into formulasin the app
this is one of 865
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