lesson
A solution can be a set of values
1 · Learn
An inequality compares values rather than saying they are equal. Solve simple inequalities using equivalent operations. Multiplying or dividing both sides by a negative reverses the inequality direction because it reverses order on the number line.
Use an open endpoint for an excluded value and a closed endpoint for an included one. If only integers are allowed, list or mark the permitted integers rather than implying every real number is acceptable.
2 · Worked example
For 2x + 1 <= 9, subtract 1 and divide by 2 to obtain x <= 4. The endpoint 4 is included because equality is allowed.
3 · Your turn
Solve 3x - 2 > 10. Is x = 4 included?
Check your answer
x > 4. No, equality at 4 does not satisfy the strict inequality.
4 · Apply your learning
Test a value below, at and above the boundary in the original inequality.
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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