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Linear Equations in One Variable Practice

Solve chapter-level practice questions for Linear Equations in One Variable with reveal-only solutions and quick revision support.

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Practice Set 1 — Solving Equations

Variable on one or both sides, brackets, and fractions.

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Q1. Solve: 5x − 3 = 3x + 11.
Q2. Solve: 2(y + 4) − 3 = 9.
Q3. Solve: x/2 + x/3 = 10.
Q4. Solve: (2x − 3)/4 = (x + 1)/3.
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Q5. Solve: 0.4(3 − x) = 0.5x − 1.

Practice Set 2 — Word Problems

Translating situations into linear equations.

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Q1. The sum of two numbers is 45 and one is twice the other. Find the numbers.
Q2. A number is increased by 12 and the result is 3 times the original number. Find the number.
Q3. The length of a rectangle is 5 cm more than its breadth and the perimeter is 50 cm. Find its dimensions.
Q4. Present ages of A and B are in the ratio 4 : 5. Five years later the ratio becomes 5 : 6. Find their present ages.
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Q5. Sum of the digits of a two-digit number is 9. If 27 is added to the number, its digits are reversed. Find the number.

Quick Q&A Before You Revise

What does 'transposing' a term mean?

Moving a term from one side of the equation to the other. When it crosses the equals sign, its sign changes (a '+' becomes '−' and vice versa). It is a shortcut for adding or subtracting the same quantity on both sides.

Why do we multiply by the LCM to solve equations with fractions?

Multiplying every term by the LCM of the denominators clears all fractions in one step, leaving a simpler equation with only whole-number coefficients.

How do I check whether my solution is correct?

Substitute the value back into the original equation. If the left-hand side equals the right-hand side, the solution is correct.

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