Simple Equations Class 7 Notes CBSE Maths Chapter 4 (Free PDF Download)

• The value of a variable can take on a variety of numerical values whose value is not fixed. 

• Variables can be represented as alphabetical letters such as $\text{a, b, c, x, y, z}$ etc.

• Expressions are made up of variables.

• The expressions are created by performing operations on the variables such as addition, subtraction, multiplication, and division.

• An equation is a condition on a variable that demands that two expressions in the variable have the same value.

• The solution of the equation is the value of the variable for which the equation is satisfied.

• If the $\text{LHS}$ and $\text{RHS}$ are swapped or interchanged, the equation remains the same.

• In the case of the balanced equation, if we

1. Add the same number to both the sides, or 

2. Subtract the same number from both sides, or

3. Multiply both sides by the same number, or

4. Divide both sides by the same number, the balance remains undisturbed, i.e., the value of the $\text{LHS}$ remains equal to the value of the $\text{RHS}$.

Example:

Consider an equality $\text{16 - 5 = 8 + 3}$.

Solution:

The above equality holds, since both its sides are equal (each is equal to $\text{11}$).

1. Let us now add $3$ to both sides; as a result

$\text{LHS = 16 - 5 + 3}$

$\text{LHS = 11 + 3}$

$\text{LHS = 14}$

$\text{RHS = 8 + 3 + 3}$

$\text{RHS = 11 + 3}$

$\text{RHS = 14}$

That is 

$\text{LHS = RHS}$ , Here equality holds.

2. Let us now subtract $3$ to both sides; as a result

$\text{LHS = 16 - 5 - 3}$

$\text{LHS = 11 - 3}$

$\text{LHS = 8}$

$\text{RHS = 8 + 3 - 3}$

$\text{RHS = 8}$

That is 

$\text{LHS = RHS}$ 

Here equality holds.

3. Let us now multiply by $5$ to both sides; we get

$\text{LHS = }\left( \text{16 - 5} \right)\times 5$

$\text{LHS = 11}\times 5$

$\text{LHS = 55}$

$\text{RHS = }\left( \text{8 + 3} \right)\times \text{5}$

$\text{RHS = 11}\times \text{5}$

$\text{RHS = }55$

That is 

$\text{LHS = RHS}$ 

Here equality holds.

4. Let us now divide by $5$ to both sides; we get

$\text{LHS = }\left( \text{16 - 5} \right)\div 5$

$\text{LHS = 11}\div 5$

$\text{LHS = }\dfrac{11}{5}$

$\text{RHS = }\left( \text{8 + 3} \right)\div \text{5}$

$\text{RHS = 11}\div \text{5}$

$\text{RHS = }\dfrac{11}{5}$

That is 

$\text{LHS = RHS}$ 

Here equality holds.

• The equality may not hold if we do not do the same mathematical operation with the same integer on both sides of an equivalence.

• The above property provides a method for solving an equation in a systematic manner. 

On both sides of the equation, we perform a series of identical mathematical operations in such a way that one side yields only the variable. 

The equation's solution is the final step.

• Changing the side of a number (that is transposing it) is the same as adding or subtracting the number from both sides.

• Moving to the opposite side is referred to as transposing. 

• The effect of transposing a number is the same as adding (or removing) the same number to both sides of the equation.

• You can change the sign of a number when you move it from one side of an equation to the other.

Example:

In the equation $\text{y - 7 = 15}$, transposing $\text{- 7}$ from the $\text{LHS}$ to the $\text{RHS}$ which gives,

$\text{y = 15 + 7}$

$\text{y = 22}$

• The transposition of an expression can be done in the same way that the transposition of a number can be done.

• We learned how to write simple algebraic expressions that correspond to real-life situations.

• We also learned how to build an equation from its solution by employing the concept of doing the same mathematical operation (for example, adding the same integer) on both sides. 

• We also learned that we might apply a given equation to a specific practical scenario and use the equation to create a practical word problem or puzzle.

Example:

1. Nita’s father’s age is $10$ years more than twice times Nita’s age. Find Nita’s age, if her father is $\text{54}$ years old.

Solution:

Consider Nita’s age will be $\text{x}$

We know that, Nita’s father’s age is $10$ years more than twice times Nita’s age and now he is $\text{54}$ years old.

Therefore, we can express as;

$\text{2x + 10 = 54}$

By transposing $\text{+ 10}$ from $\text{LHS}$ to $\text{RHS}$, we get

$\text{2x = 54 - 10}$

$\text{2x = 44}$

$\text{   x = }\dfrac{44}{2}$

Hence,

$\text{   x = 22}$

Therefore, Nita’s age is $\text{22}$ years.

Simple Equations Class 7 Notes Maths Chapter 4- PDF Download

Let’s revise the concepts in the chapter briefly:

Simple Equations

A simple equation is the set of variables, constants, and mathematical operations like addition, subtraction, multiplication, or division which are balanced by an equal sign. The left side of the equation is called the left-hand side (LHS) and the right side of the equation is called the right-hand side (RHS). 

Consider an example x + 3 = 8. So, this letter x which is unknown is said to be a variable. A variable can be represented by any letter from a to z. We can write a general equation in one variable x in the form of ax+b=c

Here the Variable ‘a’ Represents the Coefficient of x, and the Variables b and c Represents the Constant Term

• Variables: The letters used to express the unknown values are known as variables. 

• Constants: Constants are the values that remain constant throughout the solution. In other words, it is a symbol that has any fixed numeric value.

Equal to Sign: An equal to sign represents the balanced status between the left-hand-side(LHS) and the right-hand-side(RHS) of the equation.

Solving Simple Equations

In many cases solving simple equations requires rearrangement. This means that we need to move all the terms or numbers to one side of the equality symbol (such as =, >, or <) and x on the other side of the equality symbol. We can also refer to this process as isolating x.

We Can Always Rearrange the Equations for Solving Simple Equations Using a Set of Extremely Simple Rules:

1. Whatever we do to one side of the equation, we must do the same to the other. That way you preserve the relationship between them. It doesn’t matter what you do, whether it’s take away 2, add 57, multiply by 150, or divide by x.

2. As long as we do operations on both sides, the equation remains correct. It can help to think of your equation as a set of scales or a see-saw, which must always balance.

3. Solving simple equations is also done according to the BODMAS rule. So always remember to do the calculation in the right order.

4. Make equations as simple as possible: multiply the brackets, divide, cancel out the fractions, and add or subtract all the like terms.

Advantages of  Revision Notes of CBSE Class 7 Chapter 4 

Following are the advantages of referring to the Revision Notes by Vedantu: 

• Students will be able to revise the important concepts and formulas. 

• Students can have a quick revision of all the topics of this chapter which are important from an exam point of view.

• The revision notes are very essential for last-minute examination preparation.

• Studying from revision notes will minimise chances of making simple, but conspicuous mistakes

• These revision notes are highly beneficial as all the important topics of CBSE Class 7 Maths Notes of Simple Equations are covered systematically in this PDF.

Conclusion

"Simple Equations Class 7 Notes CBSE Maths Chapter 4 [Free PDF Download]" plays a pivotal role in shaping students' mathematical acumen. This chapter serves as a crucial stepping stone in the realm of algebra, introducing students to the essential concept of solving equations. These free PDF notes provide a comprehensive and accessible resource, making quality education available to a wider audience. Beyond academic excellence, the significance of these notes lies in their ability to nurture critical thinking, problem-solving skills, and logical reasoning. They empower students to approach real-world challenges with mathematical precision, equipping them with lifelong skills that extend far beyond the classroom.