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Subjects /Class 7 / Mathematics.7 / Simple Equations

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INTRODUCTION
28 Sep 2021

An equation is a condition on a variable.

A variable is something that can vary.

It assumes different numerical values; its value is not fixed.

These are usually denoted by letters of the English alphabet, such as x, y, z, l, m, n, p, etc.

Equations and Balanced Equations

Equation

  • An equation is a condition on a variable. It says that two expressions are equal.

Algebraic Expressions:

  • It is an expression involving constant, variable and some operations like addition, multiplication etc.

What are the procedures to solving an equation:

1. Add the same number to both sides,

                            OR

2. Subtract the same number from both sides,

                            OR

3. Multiply by the same number to both sides,

                            OR

4. Divide by the same number both its sides, the balance is undisturbed.

Important Points Related to the Equation

  • One of the expressions must have a variable.
  • LHS of the equation is equal to the RHS of the equation.
  • An expression does not have equality sign but an equation always has an equality sign.
  • If we interchange the position of the expression from LHS to RHS or vice versa, the equation remains the same.

4x + 8 = 3

3 = 4x + 8

Both the above equations are same.

How to form equations using statements?

This is the most difficult part of simple equations for students.

Let us learn some important points before making equations:

  • Carefully read the statement first.
  • Break it into two parts:
    • The first part contains the variable, operation like +, - , ×, \(\divide\) along with the constant. It is called the LHS.
    • The Second part forms the equal to part. This is called the RHS.
  • Now, First make a meaning full LHS using the variable, constant and the operator between them.
  • Important thing is to try to understand the question, make a rough idea of the statement
  • For example:
    • The sum of five times of x and 13 means
    • Sum \(\Rightarrow\) +
    • Five times of x \(\Rightarrow\) 5 × x = 5x
    • Sum of five times x and 13 \(\Rightarrow\) 5x + 13
  • Now, Search for the RHS part of the question:
  • For example:
    • Is equal to 45 means
    • Equal \(\Rightarrow\) =
    • Equal to 45 \(\Rightarrow\) = 45
  • So, join the LHS and the RHS part and your equation is ready.

For example: The sum of five times of x and 13 is equal to 45.

5x + 13 = 45

Define Balanced Equation:

  • When the LHS = RHS of an equation, then it is said to be a balanced equation.

What do you mean by Transposing?

  • Transposing means moving to the other side. It has the same effect as adding the same number to (or subtracting the same number from) both sides of the equation.
  • When we transpose a number from one side of the equation to the other side, we change its sign.

NCERT SOLUTIONS

EXERCISE 4.1

 1. Complete the last column of the table.

S.No

Equation

Value

Say, whether the equation is satisfied. (Yes/No)

(i)

x + 3 = 0

x = 3

 

(ii)

x + 3 = 0

x = 0

 

(iii)

x + 3 = 0

x = -3

 

(iv)

x + 3 = 0

x = 7

 

(v)

x – 7 = 1

x = 8

 

(vi)

5x = 25

x = 0

 

(vii)

5x = 25

x = 5

 

(viii)

5x = 25

x = -5

 

(ix)

(m/3) = 2

m = -6

 

(x)

(m/3) = 2

m = 0

 

(xi)

(m/3) = 2

m = 6

 


Solution:

S.No

Equation

Value

Say, whether the equation is satisfied. (Yes/No)

(i)

x + 3 = 0

x = 3

No

(ii)

x + 3 = 0

x = 0

No

(iii)

x + 3 = 0

x = -3

Yes

(iv)

x + 3 = 0

x = 7

No

(v)

x – 7 = 1

x = 8

Yes

(vi)

5x = 25

x = 0

No

(vii)

5x = 25

x = 5

Yes

(viii)

5x = 25

x = -5

No

(ix)

(m/3) = 2

m = -6

No

(x)

(m/3) = 2

m = 0

No

(xi)

(m/3) = 2

m = 6

Yes

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

(a) n + 5 = 19 (n = 1)

(b) 7n + 5 = 19 (n = 2)

(c) 7n + 5 = 19 (n = 2)

(d) 4p – 3 = 13 (p = 1)

(e) 4p – 3 = 13 (p = –4)

(f) 4p – 3 = 13 (p = 0)
Solution:

(a) \(1+5=19(\mathrm{n}=1)\) Put \(\mathrm{n}=1\) in LHS \(1+5=6 \neq 19(\mathrm{RHS})\) Since LHS \(\neq \mathrm{RHS}\)

Thus \(\mathrm{n}=1\) is not the solution of the given equation.

(b) \(7 \mathrm{n}+5=19 ;(\mathrm{n}=-2)\)

Put \(\mathrm{n}=-2\) in LHS

\(7 \times 2+5=14+5=-9 \neq 19\) (RHS)

Since LHS \(\neq\) RHS

Thus, \(\mathrm{n}=-2\) is not the solution of the given equation.

(c) \(7 \mathrm{n}+5=19 ;(\mathrm{n}=2)\)