Topic Details (Notes format)

How to Solve Linear Equations (Single Variable)

Subject: Mathematics

Book: Maths Mastery

Solving linear equations with one variable is a foundational algebraic skill. These typically appear in the form ax + b = c, where x is the variable to solve for. The key steps involve isolating x by reversing operations in a structured manner: subtract or add constants from both sides, then multiply or divide by the coefficient. For example, in 3x + 4 = 16, subtract 4 from both sides to get 3x = 12, then divide by 3 to find x = 4. Linear equations model numerous real-life situations, such as budgeting daily expenses, calculating distances, and analyzing rates. Proficiency with them paves the way for advanced mathematics like systems of equations and polynomials.

Practice Questions

What is the value of x if 3x + 7 = 16?

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A man spends 75% of his income and saves Rs. 600. What is his total income?

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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 man rows downstream at 6 km/h and upstream at 4 km/h. What is the speed of the stream?

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If x^2 + 4x + 4 = 0, what is the value of x?

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If a:b = 5:7 and b:c = 6:11, what is a:c?

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What is the HCF of 48 and 180?

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If a cone has a radius of 5 cm and a height of 12 cm, what is its slant height?

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If x = 3 and y = 4, what is the value of x^2 + y^2?

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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