This article covers the essential skills of solving linear equations in one unknown – a core topic in DSE Paper 1 Section A(1) worth 3–5 marks. You will learn the transposition method for solving equations, how to handle equations with fractions and decimals, how to translate word problems into linear equations, and how to identify special cases (unique solution, no solution, and infinite solutions). The article includes step-by-step worked examples, DSE exam techniques, practice questions, and a full set of homework with solutions. These are essential skills that appear in almost every DSE paper.
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Linear Equations in One Unknown | Complete Guide
Question 1 MC
Solve \( 3x + 7 = 28 \).
A. \( 5 \) B. \( 7 \) C. \( 9 \) D. \( 11 \)
Question 2 MC
Solve \( \frac{x}{4} - 2 = 3 \).
A. \( 4 \) B. \( 8 \) C. \( 16 \) D. \( 20 \)
Question 3 Short Answer
Solve \( 0.4x + 0.3 = 1.1 \).
Question 4 Short Answer
Solve \( \frac{3x-1}{2} = \frac{x+4}{3} \).
Question 5 MC
Which equation has infinite solutions?
A. \( 2x + 3 = 7 \) B. \( 2x + 3 = 2x + 5 \) C. \( 2x + 3 = 2x + 3 \) D. \( x + 3 = 5 \)
Question 6 Short Answer
Solve \( \frac{2x-3}{4} - \frac{x+1}{2} = 1 \).
Question 7 MC
If \( 3x - 5 = 2x + 7 \), find \( x \).
A. \( 2 \) B. \( 6 \) C. \( 12 \) D. \( 14 \)
Question 8 Short Answer
The sum of two consecutive numbers is 45. Find the numbers.
Question 9 Short Answer
Solve \( 0.02x + 0.03 = 0.07 \).
Question 10 Short Answer
Solve \( \frac{2x+1}{5} - \frac{x-1}{2} = 0 \).
When solving equations with fractions, remember to multiply every term by the LCD – not just the fractions. Missing a term is a common error.