Solving linear equations
Edexcel 1MA1 examines this on every paper across both tiers. Foundation focuses on one-step and two-step equations and equations with brackets; Higher pushes into equations with unknowns on both sides, fractional coefficients, and graphical interpretation.
Algebraic methods
The aim: isolate the variable on one side. The "do the same to both sides" rule applies at every step.
One-step
x + 5 = 12 → x = 7 (subtract 5 from both sides). 3x = 18 → x = 6 (divide both sides by 3).
Two-step
2x + 5 = 17 → 2x = 12 → x = 6.
Brackets
Expand first, then collect. 3(x − 4) = 9 → 3x − 12 = 9 → 3x = 21 → x = 7.
Unknowns on both sides
Move the variable terms to one side, constants to the other. 5x + 3 = 2x + 18 → 3x + 3 = 18 → 3x = 15 → x = 5.
Fractions
Multiply both sides by the denominator (or a common multiple). (x + 1)/4 = 3 → x + 1 = 12 → x = 11.
(x − 2)/3 = (x + 4)/5 → 5(x − 2) = 3(x + 4) → 5x − 10 = 3x + 12 → 2x = 22 → x = 11.
Graphical method
To solve f(x) = g(x), plot y = f(x) and y = g(x). The x-coordinates of the intersection points are the solutions.
For a single equation set equal to zero, plot y = f(x) and read where it crosses the x-axis.
Common Edexcel mark-scheme phrasing
- M1 for a correct expansion or collection step.
- M1 for isolating the variable.
- A1 for the correct value.
- B1 for reading a solution from a graph (often with a tolerance).
⚠Common mistakes— Common errors
- Sign errors when moving terms across.
- Forgetting to multiply both terms inside brackets.
- Dividing only part of one side when isolating x.
- Stating the y-value of an intersection instead of the x-value as the solution.
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