Form equations

Objective. Translate geometric and contextual information into equations.

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2. Worked example
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Learn: the key idea

Forming equations means translating a worded or geometric description into algebraic notation, using a letter for the unknown quantity before solving it as a normal equation. For a rectangle with length (x + 3) and width x where the perimeter is 26, the equation is 2(x + 3) + 2x = 26, which expands and solves to find x. The key skill is reading the context carefully to decide what the unknown represents and how the given facts relate to each other, before writing a correct equation that captures every piece of information.

Worked example

A triangle has angles x, x + 10 and x + 20 degrees. Form equations to find the value of x.

1 $Use the angle sum fact that angles in a triangle total 180 degrees$
2 $Form the equation: x + (x + 10) + (x + 20) = 180$
3 $Simplify: 3x + 30 = 180$
4 $Solve: 3x = 150, so x = 50$

Answer: x = 50

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Common mistake. Pupils sometimes write the perimeter equation using only one pair of sides instead of both pairs, turning a rectangle perimeter problem into (x + 3) + x = 26 instead of correctly doubling both sides to get 2(x + 3) + 2x = 26.

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