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 x:y = 4:5 and y:z = 2:3, what is x:z?

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A car covers a distance of 150 km in 2.5 hours. What is its average speed?

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What is the sum of the first 50 positive integers?

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

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If a cylinder has a radius of 7 cm and height of 10 cm, what is its volume?

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What is the cube of 4?

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

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What is the sum of the interior angles of a hexagon?

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If x^2 - 6x + 9 = 0, what is the value of x?

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The LCM of 12 and 15 is:

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