Courses

Courses for Kids

Free study material

Store

Talk to our experts

1800-120-456-456

RD Sharma Solutions

RD Sharma Class 8 Solutions Chapter 9 - Linear Equation In One Variable (Ex 9.1) Exercise 9.1 - Free PDF

RD Sharma Class 8 Solutions Chapter 9 - Linear Equation In One Variable (Ex 9.1) Exercise 9.1 - Free PDF

Q: 4. What is a common mistake to avoid when solving problems from Exercise 9.1?

A very common mistake is an error in sign change during transposition. Students often forget to change the sign of a term when moving it across the equals sign or incorrectly handle negative signs when simplifying. Always double-check that every term moved has its sign correctly inverted to prevent this error.

Q: 5. What is the difference between a linear 'expression' and a linear 'equation' in this chapter?

A linear expression is a combination of variables and constants without an equals sign, such as '3x - 7'. An equation, however, is a statement that sets two expressions equal to each other, like '3x - 7 = 5'. The goal of solving an equation is to find the specific value of the variable that makes this statement true.

Preparation for Class 8 with RD Sharma Solutions

Free PDF download of RD Sharma Class 8 Maths Solutions Chapter 9 - Linear Equation In One Variable Exercise 9.1 solved by Expert Mathematics Teachers on Vedantu. All Chapter 9 - Linear Equation In One Variable Ex 9.1 Questions with Solutions for RD Sharma Class 8 Maths to help you to revise complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other Engineering entrance exams.

Vedantu is a platform that provides free NCERT Solution and other study materials for students. Science Students who are looking for NCERT Solutions for Class 8 Science will also find the Solutions curated by our Master Teachers really Helpful.

Introduction

In this Chapter, you will be taught algebraic equations and expressions. We will be dealing with linear expressions in one variable only. Thus, such equations are known as linear equations in one variable.

These are of the format shown below:

Equations

5x + 2 = 7
x =17
7y +1 = 8

We can clearly see that equations have an equality sign (=), which is not found in expressions from the illustrations.

Variables, constants, and some mathematical operations like addition or multiplication are involved in an algebraic expression.

An expression that equates two expressions is an equation.

Some Points We Must Keep in Our Mind:

An equality involving variables is called an algebraic equation. It will always have an equality sign. The part to the left of the equality sign is called the Left Hand Side or (LHS). The part to the right of the equality sign is called the Right Hand Side or (RHS).
The values of the expressions on the LHS and RHS will always be equal in an equation. This is valid only for some values of the variable. These values are known as the solutions to the equation.
In order to find the solution to an equation, we assume two sides of the equation to be balanced. We then do the same operations on both sides of the equation to get the solution.

Some of the Topics which are discussed in this Chapter are as Follows

Equations With Linear Expression on One side and Numbers on the Other Side
Some Applications
Equations that Have Variables on Both Sides
Reducing Equations to Simpler Forms

Equations With Linear Expression on One side and Numbers on the Other Side

Let us learn this topic by solving equations like the one shown below:

5y - 12 = 8

To solve, will by add 12 on both sides:

5y - 12 + 12 = 8 + 12

5y = 20

Hence,

y = 4

The above example is a linear expression with the highest power of a variable as only 1. There can be one or more than one variable in a linear equation.

Some Applications

There are applications of linear equations. They help us in the real world. There are many examples that involve some real-life situations like counting money, calculating age, finding perimeter and area etc.

Illustration:

Question: Alexa is twice the age of Jenna. Ten years ago her age was three times

Jenna’s age. What are their current ages?

Solution:

Let Jenna’s present age be x years.

Therefore Alexa’s present age will be 2x years.

Jenna’s age ten years ago was

(x – 10) years.

Alexa’s age ten years ago was

(2x – 10) years.

It is given that Alexa’s age ten years ago was three times Jenna’s age.

Thus,

2x – 10 = 3(x – 10)

2x – 10 = 3x – 30

3x – 2x=30 – 10

x=20

So,

Jenna’s present age x = 20 years

While,

Alexa’s present age is 2x = 2 × 20 = 40 years.

Equations that Have Variables on Both Sides

So far, we have only seen equations where the values on the right-hand side of the equality sign have been numbers. Now, let us look into questions where there are variables on both sides.

Example:

3x - 7 = x +3

Solution:

Adding 7 to both sides,

3x-7+7 =x + 3 + 7

Subtracting x from both sides we get

3x - x = x + 10 - x

2x=10

Hence,

x = 5

Reducing Equations to Simpler Forms

A complex linear equation with fractions can be reduced into simpler forms by the following steps:

First, the LCM of the denominator is taken.
Then, the RHS and LHS of the equation are multiplied both with the LCM.
Therefore, the equation gets reduced to a form without a denominator in it.

To understand this better, let us take the help of an example:

\[\frac{x}{3}-\frac{1}{5}=\frac{x}{5}+\frac{1}{4}+2\]

\[\frac{5x}{15}-\frac{3x}{15}=\frac{4+5+40}{20}\]

\[\frac{2x}{15}=\frac{49}{20}\]

\[2x=\frac{49}{20}\times 15\]

\[x=\frac{49}{40}\times 15\]

\[x=\frac{147}{8}\]

Conclusion

For students who wish to score high marks in Math, RD Sharma Solutions is the best study material. The subject matter experts at Vedantu have prepared the RD Sharma solutions to help the students who are finding difficulties in solving them. Students can easily access answers to the problems present in RD Sharma Class 8 Chapter 9 by downloading the PDF. It contains all solutions in a detailed manner and also expects questions to be asked in the exam. After solving these problems students will get more confident about the exam.

FAQs on RD Sharma Class 8 Solutions Chapter 9 - Linear Equation In One Variable (Ex 9.1) Exercise 9.1 - Free PDF

1. What is the primary method used in Vedantu’s RD Sharma Solutions for solving equations in Exercise 9.1?

The primary method demonstrated in the solutions for Exercise 9.1 is transposition. This involves moving terms from one side of the equals sign to the other to isolate the variable. The key steps are:

Group all terms with the variable on one side (usually the Left-Hand Side).
Move all constant terms to the opposite side.
Change the sign of any term that is moved across the equals sign (+ becomes −, and − becomes +).
Simplify both sides to find the value of the variable.

2. How can I verify if my answer for a problem from RD Sharma Class 8 Chapter 9 is correct?

To verify your solution, you should substitute the value of the variable you found back into the original equation. Check if the Left-Hand Side (LHS) of the equation equals the Right-Hand Side (RHS). If LHS = RHS, your answer is confirmed to be correct. This is a crucial final step to ensure accuracy.

3. Why does a term's sign change when it is moved to the other side of the equation during transposition?

The changing of signs during transposition is a shortcut for the fundamental rule of balancing equations: performing the same operation on both sides. For instance, to remove a '+4' from one side, you must subtract 4 from both sides. This action cancels the '+4' on the original side and makes it appear as '−4' on the other. Transposition is just a faster way to apply this principle.

4. What is a common mistake to avoid when solving problems from Exercise 9.1?

A very common mistake is an error in sign change during transposition. Students often forget to change the sign of a term when moving it across the equals sign or incorrectly handle negative signs when simplifying. Always double-check that every term moved has its sign correctly inverted to prevent this error.

5. What is the difference between a linear 'expression' and a linear 'equation' in this chapter?

A linear expression is a combination of variables and constants without an equals sign, such as '3x - 7'. An equation, however, is a statement that sets two expressions equal to each other, like '3x - 7 = 5'. The goal of solving an equation is to find the specific value of the variable that makes this statement true.

6. How do the RD Sharma solutions help in tackling equations that involve fractions?

The solutions demonstrate a key strategy for handling fractions: find the Least Common Multiple (LCM) of all the denominators in the equation. By multiplying every term on both sides of the equation by the LCM, you can eliminate the fractions entirely. This transforms the problem into a simpler linear equation with whole numbers, which is easier to solve.

7. How are the concepts from Chapter 9, 'Linear Equation in One Variable,' applied in real-life situations?

Linear equations are fundamental to solving many real-world problems. They can be used to model situations involving:

Calculating distances, speeds, and times.
Solving problems related to age, money, and measurement.
Figuring out unknown quantities in geometry, such as the dimensions of a perimeter.
Making financial calculations for profit, loss, and interest.

This chapter builds the foundation for translating such scenarios into solvable mathematical forms.