NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations Exercise 4.3

Welcome to CBSE Class 7 Maths, where we explore the power of Simple Equations! In Chapter 4, Exercise 4.3, we transition from the basic balancing method to the highly efficient Transposition Method. This exercise is one of the most critical parts of your algebra journey because it teaches you how to quickly shift terms across the equals sign to isolate the variable. By mastering Exercise 4.3, you will learn to solve equations with brackets, fractions, and negative integers step-by-step. At YoLearn.ai, we make learning intuitive. Instead of memorizing rules, our AI Tutor helps you visualize how operations reverse when they jump across the equal boundary. Whether you are dealing with fractional variables or clearing out nested parentheses, this guide provides crystal-clear breakdowns, visual processes, and hand-picked practice problems designed to help you score full marks. Let's grab your notebook and master this chapter together!

Introduction to the Transposition Method

In our previous exercises, we solved equations by performing the same arithmetic operation on both sides of the equal sign ($=$). While that balancing method is mathematically beautiful, it can become tedious. In Simple Equations Exercise 4.3, we introduce the Transposition Method.

Transposition simply means moving a number or variable from one side of an equation to the other side. When a number 'crosses' the equals sign, its sign changes to its opposite (inverse) mathematical operation. This makes equation-solving significantly faster. For instance, addition turns into subtraction, subtraction turns into addition, multiplication turns into division, and division turns into multiplication.

The Golden Rules of Transposition

  1. Identify the target — Look at the equation and decide which term needs to be moved to isolate the variable (usually keeping variables on LHS and constants on RHS).
  2. Change addition to subtraction — If a positive number is added on one side, it becomes subtracted when transposed to the other side. Example: $x + 5 = 12$ becomes $x = 12 - 5$.
  3. Change subtraction to addition — If a number is subtracted on one side, it becomes added on the other side. Example: $y - 3 = 8$ becomes $y = 8 + 3$.
  4. Change multiplication to division — If a number multiplies the variable, transposing it makes it divide the opposite side. Example: $4z = 20$ becomes $z = \frac{20}{4}$.
  5. Change division to multiplication — If a number divides the variable, transposing it makes it multiply the opposite side. Example: $\frac{p}{5} = 6$ becomes $p = 6 \times 5$.

Step-by-Step Worked Examples

  • Example 1: Solve $2y + \frac{5}{2} = \frac{37}{2}$ Step 1: Transpose the constant term $+\frac{5}{2}$ to the RHS as subtraction: $2y = \frac{37}{2} - \frac{5}{2}$ Step 2: Simplify the fractions on the RHS: $2y = \frac{37 - 5}{2} = \frac{32}{2} = 16$ Step 3: Transpose 2 (which multiplies $y$) to RHS as division: $y = \frac{16}{2}$ $y = 8$ Final Answer: $y = 8$
  • Example 2: Solve $5t + 28 = 10$ Step 1: Transpose $+28$ to RHS as $-28$: $5t = 10 - 28$ Step 2: Simplify the subtraction: $5t = -18$ Step 3: Transpose 5 to RHS as division: $t = -\frac{18}{5}$ Final Answer: $t = -\frac{18}{5}$
  • Example 3: Solve the equation with brackets: $2(x + 4) = 12$ Step 1: First, transpose the multiplier 2 from LHS to RHS as division: $x + 4 = \frac{12}{2}$ Step 2: Simplify the RHS: $x + 4 = 6$ Step 3: Transpose $+4$ to RHS as $-4$: $x = 6 - 4$ $x = 2$ Final Answer: $x = 2$

Exam Trap: Watch out for Sign Changes!

A very common mistake students make is changing the sign of a coefficient when dividing.

  • Correct: If $-3x = 15$, then transposing $-3$ yields $x = \frac{15}{-3} = -5$. Notice that the negative sign stayed with the 3 during division.
  • Incorrect: Writing $x = \frac{15}{3} = 5$.

Remember, when you transpose a multiplying coefficient, you change the operation from multiplication to division; you do not change its negative sign to positive!

Practice Questions with Solutions

  • Q: Solve the equation: $\frac{q}{4} + 7 = 5$ A: Step 1: Transpose $+7$ to the RHS as $-7$: $\frac{q}{4} = 5 - 7$ Step 2: Simplify the RHS: $\frac{q}{4} = -2$ Step 3: Transpose the denominator 4 to the RHS as multiplication: $q = -2 \times 4$ $q = -8$ Final answer: $q = -8$
  • Q: Solve the equation: $3s + 12 = 0$ A: Step 1: Transpose $+12$ to the RHS as $-12$: $3s = 0 - 12$ $3s = -12$ Step 2: Transpose 3 to the RHS as division: $s = \frac{-12}{3}$ Step 3: Simplify the division: $s = -4$ Final answer: $s = -4$
  • Q: Solve the bracket equation: $3(2 - x) = 15$ A: Step 1: Transpose the multiplier 3 to the RHS as division: $2 - x = \frac{15}{3}$ $2 - x = 5$ Step 2: Transpose $+2$ to the RHS as $-2$: $-x = 5 - 2$ $-x = 3$ Step 3: Multiply both sides by $-1$ to isolate $x$: $x = -3$ Final answer: $x = -3$
  • Q: Solve: $16 = 4 + 3(t + 2)$ A: Step 1: Transpose $+4$ to the LHS as $-4$: $16 - 4 = 3(t + 2)$ $12 = 3(t + 2)$ Step 2: Transpose the multiplier 3 to the LHS as division: $\frac{12}{3} = t + 2$ $4 = t + 2$ Step 3: Transpose $+2$ to the LHS as $-2$: $4 - 2 = t$ $2 = t$ (or $t = 2$) Final answer: $t = 2$

Frequently Asked Questions

Can I solve bracket equations by opening the brackets first?

Yes, you can. For example, in $2(x+4)=12$, you can distribute 2 to get $2x + 8 = 12$. Transposing 8 gives $2x = 4$, which simplifies to $x = 2$. Both methods yield the exact same answer.

What is the basic rule of transposition?

The basic rule is that when any term moves across the equal sign, its operation reverses. Addition becomes subtraction, subtraction becomes addition, multiplication becomes division, and division becomes multiplication.

How do I check if my final answer to a simple equation is correct?

You can verify your answer by substituting the value of the variable back into the original equation. If the Left Hand Side (LHS) equals the Right Hand Side (RHS), your answer is 100% correct.