Topic Details (Notes format)

How to Solve Inequalities (Single Variable)

Subject: Mathematics

Book: Maths Mastery

Inequalities define ranges of possible solutions rather than a single value, typically seen in forms like ax + b < c. Solving them mirrors linear equation methods—subtracting, adding, multiplying, or dividing—while noting that multiplying or dividing by a negative number reverses the inequality sign. For instance, to solve –2x + 4 > 10, first subtract 4 from both sides, getting –2x > 6; then dividing by –2 flips “>” to “<”, yielding x < –3. Inequalities underpin budgeting constraints, capacity limits, or speed restrictions, making them critical for real-life logic and advanced fields like optimization.

Practice Questions

If x² - 9x + 18 = 0, what are the roots of the equation?

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If the perimeter of a square is 36 cm, what is the length of its diagonal?

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If x = 2 and y = 3, what is the value of (x^2 + y^2)?

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What is the HCF of 48 and 180?

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The probability of getting an even number when rolling a die is:

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If 3x = 81, what is the value of x?

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If a square has a perimeter of 64 cm, what is its area?

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The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

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What is the sum of all angles in a hexagon?

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If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

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