lesson
Unknown terms can be collected too
1 · Learn
An equation can have unknown terms on both sides. Subtract the same expression from both sides to collect them, then isolate the unknown. Expanding a bracket first may make the terms easier to see.
Keep each line equivalent and check the solution in both original sides. A value making only one rearranged fragment true is not a solution of the whole equation.
2 · Worked example
5x + 2 = 2x + 17 gives 3x + 2 = 17, then 3x = 15 and x = 5. Both original sides equal 27.
3 · Your turn
Solve 4(x + 2) = 2x + 18.
Check your answer
4x + 8 = 2x + 18, so 2x = 10 and x = 5. Both sides are 28.
4 · Apply your learning
Create a balance explanation for each step and identify which operation preserves equality.
Adult guidance and safety
Ask for the reasoning and a check, not only a numerical result. Supply accurate diagrams, coordinate grids and data displays where required. Use varied examples and revisit prerequisite gaps; these short teaching models are not a completed assessment programme.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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