lesson
Keep the balance while isolating the unknown
1 · Learn
Solving an equation finds values that make it true. Apply the same valid operation to both sides to preserve equality. For a linear equation, undo added constants and multiplied coefficients in a sensible order.
Check the solution in the original equation, not only in the final line of your working. An arithmetic slip can otherwise remain hidden.
2 · Worked example
5x + 4 = 24 gives 5x = 20, then x = 4. Substitution gives 5 × 4 + 4 = 24.
3 · Your turn
Solve 3x - 7 = 14 and check.
Check your answer
3x = 21, so x = 7. Check: 21 - 7 = 14.
4 · Apply your learning
Write a short context represented by the equation and state what x measures.
Adult guidance and safety
Require a reasoned method and an independent check. Use accurate number lines, geometric drawings and data displays where the task needs them. These text models require varied practice and diagnostic assessment before curriculum approval.
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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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