# NCERT Solutions for Class 7 Maths Chapter 4 Exercise 4.1

NCERT Solutions for Class 7 Maths Chapter 4 Exercise 4.1 (Ex. 4.1) Simple Equations updated for academic session 2021-2022 free to download in PDF file format. All the solutions are question answers are based on latest NCERT Books issued for 2021-2022.

In class 7 math exercise 4.1 we will learn to format simple linear equations in one variable. Exercise 4.1 also provides the way to solve the simple linear equations in one variable.## Class 7 Maths Chapter 4 Exercise 4.1 Solution

### CBSE NCERT Class 7 Maths Chapter 4 Exercise 4.1 Solution in Hindi and English Medium

Class: 7 | Mathematics |

Chapter: 4 | Simple Equations |

Exercise: 4.1 | Hindi and English Medium Solutions |

### Class 7 Maths Chapter 4 Exercise 4.1 Solution in Videos

#### Linear Equation

Linear equations are those equations that are of the first order. These equations are defined for lines in the coordinate system.

For example:

(i) 5 less than twice a number x can be written as 2x – 5.

(ii) One sixth of a number x can be written as.

(iii) Three times of the sum of x and 7 can be written as 3 x (x + 7).

###### Now consider the following statements:

(i) 6 more than a number x is 13 can be written as x + 6 = 13.

(ii) times a number n is 15 can be written as = 15.

(iii) A number y divided by 7 gives 5 can be written as = 5.

In each of the above statements the symbol ‘=’ (is equal to) appears. A statement involving symbol ‘=’ is called a statement of equality.

#### Equation

A statement of equality which involves one or more variables is called an equation. The expression to the left side of the equality sign (=) is called the left hand side (L.H.S.) and that of right side to the equality sign is called right hand side (R.H.S.) of the equation.

##### Linear Equation:

An equation in which the highest power of the variables is one, is called a linear equation.

Example: Equations 2x + 4 = 6, (y/3) + 1 = 2 and 2z + 5/2 = 37/2 are linear equations.

##### Solution of an Equation:

The value of unknown variable which statistics equality of both sides of the equation is known as the solution or root of the equation.

Let us verify that x = 3 is the solution (root) of the equation 4x + 6 = 18.

L.H.S. = 4x + 6 For x = 3 L.H.S. = 4 x 3 + 6 = 12 + 6 = 18 = R.H.S.

Hence, x = 3 is the solution of the equation 4x + 6 = 18.

##### Rules of solving an equation:

(i) The same quantity can be added to both sides of an equation without changing the equality.

(ii) The same quantity can be subtracted from both sides of an equation without changing the equality. (iii) Both sides of an equation may be multiplied by the same nonzero number without changing the equality.

(iv) Both sides of an equation may be divided by the same nonzero number without changing the equality.

### Class 7 Maths Exercise 4.1 Important Questions

##### How does linear equations relate to real life?

Almost any situation where there is an unknown quantity can be represented by a linear equation, like figuring out income over time, calculating mileage rates, or predicting profit. Many people use linear equations every day, even if they do the calculations in their head without drawing a line graph.

##### What are the three methods used to solve linear equations?

There are three ways to solve systems of linear equations: substitution, elimination, and graphing. Let’s review the steps for each method.

##### What are the applications of linear equations?

Applications of Linear Equations:

Solve word problems involving relationships between numbers. Solve geometry problems involving perimeter. Solve percent and money problems including simple interest. Set up and solve uniform motion problems.

##### Solve: 5x – 6 = 4x – 2.

We have:

5x – 6 = 4x – 2

Or, 5x – 4x = – 2 + 6 [transposing 4x to LHS and -6 to RHS]

Or, x = 4.

Thus, x = 4 is a solution of the given equation.