CBSE Class 7 Mathematics Chapter 4: Simple Equations NCERT Solutions

Reviewed by NCERT Help Editorial Team · Updated on 29 Jul 2026

NCERT Solutions PDF Class 7 PDF

CBSE Class 7 Mathematics Chapter 4 delves into the foundational concepts of simple equations. This chapter explains what an equation is, the meaning of its solution, and how to verify if a particular value satisfies the equation. The NCERT Solutions offer detailed, step-by-step guidance for tackling problems in Exercise 4.1, emphasizing the crucial skill of checking solutions by substituting values. These resources are crafted to establish a robust understanding of basic algebraic manipulation and problem-solving techniques, which are vital for students' ongoing mathematical development. By working through these solutions, students can effectively practice the verification process, solidifying their grasp of simple equations for confident exam preparation.

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Board	CBSE
Class	Class 7
Subject	Mathematics
Session	2026
Language	English
Type	NCERT Solutions
Chapter	Chapter 4

Chapter summary

Chapter 4, Simple Equations, for Class 7 Mathematics focuses on the basic principles of algebraic equations. The NCERT Solutions cover exercises that involve completing tables to check if given values satisfy equations and verifying if specific values are solutions to given equations. The emphasis is on the substitution method to test the validity of a potential solution.

Learning outcomes

Understand the concept of a simple equation.
Verify if a given value is a solution to an equation.
Substitute values into equations to check for satisfaction.
Identify the Left Hand Side (LHS) and Right Hand Side (RHS) of an equation.
Differentiate between a solution and a non-solution.

Topics covered

Paper topics

Introduction to Simple Equations
Understanding Equations
Checking Solutions
Substitution Method
LHS and RHS
Satisfying Equations
Table Completion for Equations

Important topics

Verifying Solutions
Substitution Method
LHS vs RHS Comparison
Identifying Equation Satisfaction

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Questions and Solutions

Question 1

Complete the last column of the table for the given equations and values.

Equation: $x + 3 = 0$ , Value: $x = 3$
Equation: $x + 3 = 0$ , Value: $x = 0$
Equation: $x + 3 = 0$ , Value: $x = -3$
Equation: $x - 7 = 1$ , Value: $x = 7$
Equation: $x - 7 = 1$ , Value: $x = 8$
Equation: $5x = 25$ , Value: $x = 0$
Equation: $5x = 25$ , Value: $x = 5$
Equation: $5x = 25$ , Value: $x = -5$
Equation: $\frac{m}{3} = 2$ , Value: $m = -6$
Equation: $\frac{m}{3} = 2$ , Value: $m = 0$
Equation: $\frac{m}{3} = 2$ , Value: $m = 6$

Solution:

To complete the table, we substitute the given value of the variable into the equation and check if the Left Hand Side (LHS) equals the Right Hand Side (RHS).

Equation: $x + 3 = 0$ , Value: $x = 3$ LHS = $3 + 3 = 6$ . RHS = 0. Since $6 \neq 0$ , the equation is not satisfied. No.
Equation: $x + 3 = 0$ , Value: $x = 0$ LHS = $0 + 3 = 3$ . RHS = 0. Since $3 \neq 0$ , the equation is not satisfied. No.
Equation: $x + 3 = 0$ , Value: $x = -3$ LHS = $-3 + 3 = 0$ . RHS = 0. Since $0 = 0$ , the equation is satisfied. Yes.
Equation: $x - 7 = 1$ , Value: $x = 7$ LHS = $7 - 7 = 0$ . RHS = 1. Since $0 \neq 1$ , the equation is not satisfied. No.
Equation: $x - 7 = 1$ , Value: $x = 8$ LHS = $8 - 7 = 1$ . RHS = 1. Since $1 = 1$ , the equation is satisfied. Yes.
Equation: $5x = 25$ , Value: $x = 0$ LHS = $5 \times 0 = 0$ . RHS = 25. Since $0 \neq 25$ , the equation is not satisfied. No.
Equation: $5x = 25$ , Value: $x = 5$ LHS = $5 \times 5 = 25$ . RHS = 25. Since $25 = 25$ , the equation is satisfied. Yes.
Equation: $5x = 25$ , Value: $x = -5$ LHS = $5 \times (-5) = -25$ . RHS = 25. Since $-25 \neq 25$ , the equation is not satisfied. No.
Equation: $\frac{m}{3} = 2$ , Value: $m = -6$ LHS = $\frac{-6}{3} = -2$ . RHS = 2. Since $-2 \neq 2$ , the equation is not satisfied. No.
Equation: $\frac{m}{3} = 2$ , Value: $m = 0$ LHS = $\frac{0}{3} = 0$ . RHS = 2. Since $0 \neq 2$ , the equation is not satisfied. No.
Equation: $\frac{m}{3} = 2$ , Value: $m = 6$ LHS = $\frac{6}{3} = 2$ . RHS = 2. Since $2 = 2$ , the equation is satisfied. Yes.

Question 2

Check whether the value given in the brackets is a solution to the given equation or not.

$n+5=19$ (n=1)
$7n+5=19$ (n=-2)
$7n+5=19$ (n=2)
$4p-3=13$ (p=1)
$4p-3=13$ (p=-4)
$4p-3=13$ (p=0)

Solution:

We check each equation by substituting the value in brackets into the Left Hand Side (LHS) and comparing it with the Right Hand Side (RHS).

Equation: $n+5=19$ , Value: $n=1$ LHS = $1+5=6$ . RHS = 19. Since $6 \neq 19$ , $n=1$ is not the solution.
Equation: $7n+5=19$ , Value: $n=-2$ LHS = $7(-2)+5 = -14+5 = -9$ . RHS = 19. Since $-9 \neq 19$ , $n=-2$ is not the solution.
Equation: $7n+5=19$ , Value: $n=2$ LHS = $7(2)+5 = 14+5 = 19$ . RHS = 19. Since $19 = 19$ , $n=2$ is the solution.
Equation: $4p-3=13$ , Value: $p=1$ LHS = $4(1)-3 = 4-3 = 1$ . RHS = 13. Since $1 \neq 13$ , $p=1$ is not the solution.
Equation: $4p-3=13$ , Value: $p=-4$ LHS = $4(-4)-3 = -16-3 = -19$ . RHS = 13. Since $-19 \neq 13$ , $p=-4$ is not the solution.
Equation: $4p-3=13$ , Value: $p=0$ LHS = $4(0)-3 = 0-3 = -3$ . RHS = 13. Since $-3 \neq 13$ , $p=0$ is not the solution.

Common mistakes

Errors in arithmetic calculations during substitution.
Incorrectly comparing LHS and RHS values.
Confusing the variable's value with the equation's result.
Misinterpreting the 'satisfied' or 'not satisfied' condition.

Revision tips

Practice substituting values carefully, paying attention to signs.
Always compare the calculated LHS with the given RHS.
Ensure you clearly state whether the equation is satisfied or not.
Review the table format in Question 1 to organize your checks.

Practice MCQs

Q1. In the equation x + 3 = 0, if x = -3, is the equation satisfied?

Q2. For the equation x - 7 = 1, what value of x satisfies it?

Q3. In the equation 5x = 25, if x = 5, is the equation satisfied?

Q4. For the equation m/3 = 2, which value of m is a solution?

Q5. When checking n + 5 = 19 with n = 1, the LHS is calculated as:

Frequently asked questions

What is the main goal of Chapter 4: Simple Equations for Class 7 Maths?

The main goal is to introduce students to the concept of simple equations and teach them how to verify if a given value is a solution to an equation by substituting it.

How do I check if a value is a solution to an equation?

Substitute the given value for the variable into the equation. If the Left Hand Side (LHS) equals the Right Hand Side (RHS) after substitution, the value is a solution.

What does it mean for an equation to be 'satisfied'?

An equation is 'satisfied' when the value of the variable makes the statement true, meaning the expression on the LHS evaluates to the same value as the RHS.

Are the questions in Exercise 4.1 about solving equations or checking solutions?

The questions in Exercise 4.1 primarily focus on checking solutions by substituting given values into equations and completing a table to indicate satisfaction.

How can these NCERT Solutions help with exam revision?

These solutions provide clear, step-by-step methods for verifying solutions, helping students practice the core skill required for this chapter and build confidence for exams.

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