Forming and Solving Equations Worksheets — KS3
Algebra is the language of mathematics, and forming and solving equations is the key skill that underpins everything from KS3 problem-solving to GCSE. Our KS3 algebra worksheets on forming and solving equations introduce formal algebraic notation clearly and systematically, helping students transition from arithmetic thinking to algebraic reasoning.
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Key Skills Covered
Progression in Equation Solving
Our worksheets build equation-solving skills in stages: one-step equations (x + 7 = 15; 3x = 24), two-step equations (2x + 5 = 19), equations with brackets (3(x + 2) = 21), and equations with unknowns on both sides (5x + 3 = 3x + 11). Each level is introduced with a worked example showing the method of inverse operations (doing the same to both sides), before students practise independently.
Forming Equations from Word Problems
A key KS3 skill is translating a word problem into an algebraic equation. For example: "I think of a number, multiply it by 4, and add 7. The result is 35. What is my number?" becomes 4n + 7 = 35. Our worksheets include scaffolded tasks where students first identify the unknown, then write the equation, then solve it — building the full process step by step.
Sample Questions
Solve: 5x + 3 = 28
Show answer
x = 5
Solve: 3(y – 4) = 15
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y = 9
Solve: 4x + 1 = 2x + 9
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x = 4
I think of a number. I multiply it by 3 and subtract 5. The answer is 16. Form and solve an equation to find my number.
Show answer
3n − 5 = 16; n = 7
A rectangle has a perimeter of 40 cm. Its length is (2x + 1) cm and its width is (x + 2) cm. Find x.
Show answer
x = 5
More Algebra Resources for Key Stage 3
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