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Inequalities
Chapter summary, hard words and model exam answers for ICSE Class 10 Hindi.
Free online summary and notes (ICSE Class 10 Hindi). Read it here, no PDF download needed.
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Mathematics · CBSE 10 · ICSE 10 · GCSE (AQA, Edexcel, OCR)
Summary
An equation has one answer; an inequality has a whole range. x > 5 is satisfied by 6, 7, 100.5 and 5.001 - infinitely many values. That range is called the solution set. Read < and > as arrows pointing to the smaller side.
Solve an inequality the same way as an equation: do the same thing to both sides to isolate the variable. The one trap is the golden rule - if you multiply or divide by a negative number, the sign flips. Check: 2 < 6, but multiply by −1 and −2 > −6.
Three ways: a number line (open circle ○ for </>, closed circle ● for ≤/≥, shade the solution); set notation {x : x > 3}; and interval notation, round ( ) excludes, square [ ] includes - so x ≥ 3 is [3, ∞). Exams ask you to switch between them.
An x² term needs a sketch. Rearrange to make one side 0, find the roots by factorising, sketch the parabola, then read off where it is above or below the axis. Above the axis = expression > 0; below = expression < 0.
Hard words & meanings
| inequality | a statement that two expressions are not equal, using <, >, ≤ or ≥ |
| solution set | the complete collection of values that satisfy an inequality |
| strict inequality | one using < or >, where the boundary value is not included |
| compound inequality | two bounds at once, e.g. −2 < x ≤ 2 |
| interval notation | writing a range with brackets, ( ) excludes and [ ] includes the endpoint |
| number line | a line marking the boundary and shading the solution, with ○ or ● circles |
| root | a value of x that makes a quadratic expression equal to zero |
| feasible region | the set of all values satisfying a real-world constraint inequality |
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