Exercise 2.1 — Simple Equations

What Does Exercise 2.1 Cover?

Exercise 2.1 from Chapter 2 — Linear Equations in One Variable focuses entirely on solving simple equations using the transposition method. All 16 questions follow the same core technique: move (transpose) terms across the equals sign to isolate the variable. This exercise is a foundational practice set for Class 8 students preparing for board exams under CBSE, Telangana, and Andhra Pradesh syllabi.

The Transposition Method — How It Works

Transposing a term means moving it from one side of the equation to the other, changing its sign in the process. A number being added on the left becomes subtracted on the right, and a number multiplying on the left becomes dividing on the right. Always transpose constants first, then the coefficient of the variable.

After finding the solution, always verify by substituting the value back into the original equation and checking that LHS = RHS.

Solutions at a Glance — All 16 Questions

• (i) 6m = 12 → m = 12/6 = 2
• (ii) 14p = −42 → p = −42/14 = −3
• (iii) −5y = 30 → y = 30/(−5) = −6
• (iv) −2x = −12 → x = −12/(−2) = 6 (negative ÷ negative = positive)
• (v) 34x = −51 → x = −51/34 = −3/2
• (vi) n/7 = −3 → n = −3 × 7 = −21
• (vii) 2x/3 = 18 → 2x = 54 → x = 27
• (viii) 3x + 1 = 16 → 3x = 15 → x = 5
• (ix) 3p − 7 = 0 → 3p = 7 → p = 7/3
• (x) 13 − 6n = 7 → −6n = −6 → n = 1
• (xi) 200y − 51 = 49 → 200y = 100 → y = 1/2
• (xii) 11n + 1 = 1 → 11n = 0 → n = 0
• (xiii) 7x − 9 = 16 → 7x = 25 → x = 25/7
• (xiv) 8x + 5/2 = 13 → 8x = 21/2 → x = 21/16
• (xv) 4x − 5/3 = 9 → 4x = 32/3 → x = 8/3
• (xvi) x + 4/3 = 3½ → x = 7/2 − 4/3 = 13/6

Worked Example — Equation with a Fraction Coefficient

For equation (xiv): 8x + 5/2 = 13. First transpose 5/2 to the right: 8x = 13 − 5/2 = 26/2 − 5/2 = 21/2. Then transpose 8 to the right: x = 21/(2 × 8) = 21/16. Verify: 8 × (21/16) + 5/2 = 21/2 + 5/2 = 26/2 = 13. ✓

Common Mistakes to Avoid

• When transposing a negative term, its sign flips — −5y = 30 gives y = 30 ÷ (−5), not 30 ÷ 5. The answer is −6, not 6.
• Dividing two negative numbers gives a positive result — in question (iv), −12 ÷ (−2) = +6.
• When the RHS has a mixed number like 3½, always convert to an improper fraction (7/2) before operating.
• Never skip the verification step in board exams — checking LHS = RHS earns marks and catches calculation errors.
• When the variable's coefficient is a fraction (like 2x/3), transpose the denominator first (multiply both sides by 3), then transpose the numerator coefficient.

What This Exercise Prepares You For

Exercise 2.1 builds the basic transposition skill that is extended in the rest of Chapter 2, where equations become more complex — variables on both sides, equations with brackets, and equations involving fractions throughout. The same solving technique is also used extensively when forming and solving equations from word problems. For the conceptual foundation behind this exercise, revisit the Introduction to Linear Equations. These skills also connect directly to algebraic expressions and lay the groundwork for quadratic equations in Class 10.