Simple Equations: Definition, Transposition and Uses

Simple Equations: Mathematics doesn’t appear complex anymore when we handle the problems with a systematic approach that helps us find the solution easily and accurately. For Class 7 students, one such important concept is simple equations. 

Simple equations help students summarise a problem using a simple expression that is easy to interpret and resolve. 

Here we discuss simple equations with clear explanations, examples, and step-by-step methods to solve problems confidently. It helps you understand how this concept is important in academics and also in real-life situations.   

Read More: Perimeter of Rectangle

What Is a Simple Equation?

A simple equation is a mathematical expression showing relationships between different entities by developing a condition of equality. It typically contains the following components:

• A variable (usually a letter like x or y)

• One or more constants (numbers)

• Mathematical operations like addition, subtraction, multiplication, or division involving the variable and a constant

• An equal sign (=) indicates the equality between LHS and RHS.

A simple equation represents a condition and helps find the variable's value.

For example,

 A simple equation is: x + 8 = 15

It is a simple math equation involving a variable x and two constants. The given condition is that when 8 is added to a variable x, its value becomes 15. We can solve this equation by finding the value of x that satisfies this condition.

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Importance of Simple Equations in Class 7

Learning about simple equations for Class 7 NCERT helps students in different ways, as explained below:

• Approach a mathematical problem logically and systematically.

• Learn the foundation of algebraic expressions using variables and constants.

• Relate equations with real-life situations to identify and solve for the unknown quantity.

This topic is important for quick solutions to math problems, but also helps understand how it relates to everyday situations.

Read More: Quadratic Equation

Solving Simple Math Equations

Simple algebra equations represent a problem statement using variables and constants and connect them with mathematical operations. 

The variable is typically the unknown quantity, and the constants are fixed numbers or known quantities. 

A specific value of the unknown variable satisfies the equation, meaning that the two sides become equal. Here is a step-by-step approach to solving a simple equation:

Step 1: Identify the variable in the equation. It is typically denoted by x.

Step 2: Combine like terms together and simplify if possible.

Step 3: Isolate the variable and keep it on the LHS. Move constant terms to the RHS of the equation by using inverse operations.

Step 4: Solve the equation to find the value of x.

Step 5: Substitute the variable value in the original equation to verify if the condition is satisfied.

These steps will guide you in working with a simple equation and finding the value of the unknown quantity. 

Read More: Parabola Equations

Examples of Simple Equations

Let's understand the process through some simple equation examples:

Example 1:

x - 3 = 8

Step 1: Keep x on LHS and shift 3 to RHS.

x = 8 + 3

Step 2: Perform the mathematical operations to find the value of x.

x = 11

Example 2:

4x = 12

Step 1: Divide both sides by 4

 4x/4 = 12/4

Step 2: Perform the mathematical operations to find the value of x.

 x = 3 

Example 3:

x/5 = 6

Step 1: Multiply both sides by 5.

(x/5) x 5 = 6 x 5

Step 2: Perform the mathematical operations to find the value of x.

x = 30 

Example 4:

3x + 4 = 25

Step 1: Add 4 to both sides.

 3x + 4 - 4 = 25 - 4

Or, 3x = 21

Step 2: Perform the mathematical operations to find the value of x.

x = 21/3 = 7

Read More: Mixed Fraction

Solving Word Problems with Simple Equations

In class 7, students are given word problems involving an unknown quantity. 

You have to express the given condition as a simple algebraic equation and solve to find the value of the unknown variable. 

Here are a few examples:

1. A number when increased by 7 becomes 20. Find the number.

Solution:

Let the number be x.

So, the simple algebra equation will be:  x + 7 = 20

Or, x = 20 – 7 = 13

 Ans. The number is 13.

2. Twice a number is equal to 16. Find the number.

Solution:

Let the number be x.

 So, the equation will be 2x = 16

Or, x = 16 ÷ 2 = 8

Ans. The number is 8.

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Tips for Solving Simple Equations

Knowing how to write, analyse, and solve simple equations helps class 7 students easily handle mathematical problems. The important tips to solve equations accurately are as follows:

• Isolate the terms with variables and constant terms.

• Use inverse operations while shifting terms from LHS to RHS.

• Simplify the equation by doing the same operation on both sides.

• Double-check your solution by substituting the value of the variable into the equation.

These simple tips make sure you arrive at the accurate solution quickly by avoiding any errors.

What is Covered in NCERT Class 7 Chapter 4 Simple Equation? 

The simple equations in the Class 7 NCERT book introduce concepts in a structured way. It covers the following topics:

• The concept of a simple equation

• Components of an equation

• Structure of an equation

• How to solve equations using various operations

• Framing equations from word problems

• Exercises for both practice and real-life applications.

The NCERT textbook uses illustrations and daily-life examples to clarify the concepts and make the topic more interesting for young learners. 

Also read: Integers

Why Learning Simple Algebra Equations Is Important

Simple equations are not just an academic concept. They help students develop a basic understanding of patterns and relationships in algebra. It becomes useful in many situations as follows:

• Solving practical problems, like budgeting, measuring, or planning.

• Approach real-life situations with reasoning and problem-solving skills.

• Preparing effectively for competitive exams and higher-level math. 

A simple equation for Class 7 is one of the basic algebra concepts. 

When students understand the equality expressions and the method of solving for the variable, using simple equations, they can confidently handle more complex math problems. 

Practicing with more equations and word problems from the NCERT Class 7 book will help improve problem-solving and logical thinking skills. 

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