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

What is the cube root of 729?

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If 5x - 2 = 13, what is the value of x?

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What is the value of x if log(x) + log(4) = log(32)?

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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What is the square root of 0.25?

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The perimeter of a rectangle is 40 cm, and its length is 12 cm. What is its width?

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If a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?

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What is the area of a sector of a circle with radius 14 cm and central angle 90°?

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

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If the sides of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?

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