Linear equations
Linear equations are where algebra starts to feel like a puzzle with rules. Every one of them asks the same question: what number can x be so both sides stay equal? The trick is to undo what was done to x in reverse order, doing the same thing to both sides each time. Most lost marks here don't come from hard ideas. They come from small slips: dividing only one term, forgetting to hand a negative sign to every term inside a bracket, or mixing x terms with plain numbers. This topic walks through those slips in the order they usually show up. You start with isolating x in one step, move to two-step equations, then brackets, like terms and equations with x on both sides. It ends with inequalities, where one extra rule matters. Work through the pages in order, try the three practice questions on each, and check every answer by plugging it back into the original equation.
Suggested learning order
- Step 1Dividing both sides to isolate xDivide the whole of each side by the coefficient on x.
- Step 2Subtracting before dividing in two-step equationsUndo the added number first, then divide by the coefficient.
- Step 3Distributing a negative signA minus in front of brackets changes the sign of every term inside.
- Step 4Combining like termsOnly terms with the same variable and power can be added together.
- Step 5Solving with variables on both sidesMove all x terms to one side before solving.
- Step 6Flipping the inequality when dividing by a negativeMultiplying or dividing by a negative reverses the inequality.
Next topic
- Lines and slopeSlope, y = mx + b, graphing lines and solving two equations at once.
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