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 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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If a:b = 2:3 and b:c = 4:5, what is a:c?

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If a person can type 45 words per minute, how many words can they type in 2 hours?

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If sin(θ) = 0.6 and θ is acute, what is cos(θ)?

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If a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?

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If sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?

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If x + y = 10 and xy = 21, what is the value of x³ + y³?

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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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What is the greatest common divisor (GCD) of 36 and 48?

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