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

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

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What is the area of an equilateral triangle with side length 10 cm?

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If a number is divisible by 9, it is also divisible by which of the following?

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What is the cube root of 729?

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If x^3 - 3x^2 + 4 = 0, what is one root of the equation?

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

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The LCM of 12 and 15 is:

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If the average of five consecutive odd numbers is 25, what is the largest number?

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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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If a:b = 3:4 and b:c = 5:6, what is a:c?

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