IGCSE Maths / Algebraic equations
Solving linear equations revision notes
Edexcel International GCSE Maths (4MA1), chapter 5: Algebraic equations, specification point 2.4a. Free lesson.
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To solve a linear equation with x on both sides, collect the x terms on one side, then isolate x. Expand brackets first, and check your answer by substituting it into the original equation.
Collect the x terms on one side
You cannot collect x terms while they are on opposite sides of the equals sign. Subtract the smaller x term from both sides so that only one side has x. Then deal with the number joined to the x term and divide to leave x on its own. Do the same operation to both sides to keep the equation balanced. To check, put your answer into the original equation. Both sides should have the same value.
Solve an equation with x on both sides
In 5x + 4 = 3x + 12, subtract 3x from both sides. This leaves 2x on the left and no x on the right. Then undo the addition of 4, and finally divide by 2. Subtracting the smaller x term avoids having a negative number of x's.
Expand brackets before collecting terms
The number outside a bracket multiplies every term inside it. For example, 3(x + 4) becomes 3x + 12, not 3x + 4. If the bracket is expanded incorrectly, the rest of the working cannot give the correct answer. For 4(x − 3), multiply 4 by both x and −3 to get 4x − 12. A term being subtracted can be cleared by adding it to both sides. So to remove −2x from one side, add 2x to both sides.
Check by substituting your answer
Substitution means putting your answer in place of x in the original equation. If both sides give the same value, your answer checks out. For x = 4 in 5x + 4 = 3x + 12, both sides equal 24. For x = 5 in 4(x − 3) = 18 − 2x, both sides equal 8. For x = 5 in 6x − 5 = 2x + 15, both sides equal 25.