Topic Details (Notes format)

How to Graph Inequalities on the Number Line

Subject: Mathematics

Book: Maths Mastery

For one-variable inequalities like x>2, you shade all real values greater than 2 on a number line, using an open circle at 2 to indicate x cannot equal 2. If it were x≥2, you’d fill the circle at 2. This visual clarifies the solution set’s extent. Number-line graphing is fundamental for single-variable constraint representation, bridging arithmetic with geometry. In daily tasks like weight or budget limits, or advanced system constraints, understanding these representations ensures a quick, intuitive grasp of allowable solution ranges.

Practice Questions

If the sum of three consecutive integers is 96, what are the integers?

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What is the sum of the first 20 odd numbers?

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If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

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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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A cone has a base radius of 7 cm and height of 24 cm. What is its volume?

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What is the area of a circle with a diameter of 14 cm?

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The ratio of two numbers is 3:5, and their sum is 64. What are the numbers?

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What is the length of the diagonal of a square with a side length of 7 cm?

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A car travels 240 km in 4 hours. What is its average speed?

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The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

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