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Let the number be x.

Dividing the number by 2, we get x/2

When, increased by 5, it gives the expression
x/2 + 5

x/2 + 5 = 9 is the required equation.

Let present age of Rama be x years.

So, five times of his age = 5x.

According to question,

5x = x + 25

⇒ 5x – x = 25

⇒ 4x = 25

⇒ x = 25/4 = 6 1/4

Thus, at present Rama is 6 1/4 years old.

Six times a number is 10 more than the number.

6x = 10 + x

(a) If smaller number is x, the other number is 81-x or 2x

(b) The equation formed is 4x + 3 = 280

(c) The solution of the equation is x = 27

(d) The numbers are 54 and 27

(a) If Palak gets x marks, Abha gets 2x marks.

(b) The equation formed is 4x + 3x = 280

(c) The solution of the equation is x = 40

(d) Marks obtained by Abha are 80

Let the number be x.

So, thrice of the number = 3x

When it decreased by 5, we get 3x – 5

According to question,

3x – 5 = 2x + 1

⇒ 3x – 2x = 1 + 5 

⇒ x = 6

Thus, x = 6 is the required number.

Correct answer is 8, 10

Let the number be x.

So, twice of the number = 2x

On adding 9 to it, we get 2x + 9

∴ 2x + 9 = 13

⇒ 2x = 13 – 9 = 4

⇒ x = 4/2 = 2

Thus, x = 2 is the required number.

x = 3 is the solution of the equation 3x – 2 =7.

Correct answer is 6 1/4 years

Correct answer is 5 years

Correct answer is 36

Let the unknown number be x

Dividing it by 6, we get x/6.

x/6= 6

By using  transpose technique:- 

x=6×6=36

Thus, the required number is 36.

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If 5 is added to three times a number, it becomes the same as 7 is subtracted from four times the same number. This fact can be represented as 3x + 5 = 4x - 7 .

 x + 7 = 10 has the solution x = 3.

x – 0 = 4 ; when 3x = 12.

x – 1= 0 ; when 2x = 2.

(a) If smaller number is x, the other number is 60-x.(use sum)

(b) The difference of numbers in term of x is 60-2x 

(c) The equation formed is -2x = 30

(d) The solution of the equation is 15

(e) The numbers are 45 and 15

Let x is the number.

According to question x + 12 = 43

⇒ x = 43 – 12 = 31

So the number is 31.

x/4 + 9 = 19

Subtract 9 from both sides

x/4 +9 – 9 = 19 – 9

⇒ x/4 = 10 

⇒ x = 10 x 4 = 40

4x + 15 = 42

Let the number be x

According to question,

5x + 2 = 42

⇒ 7x = 42

⇒ x = 42/7 = 6

So, the number is 6.

Since, square has all sides equal

∴ 18x – 20 = 42 – 13x

⇒ 18x + 13x = 42 + 20

⇒ 31x= 62

⇒ x = 62/31 = 2

∴ Side of square = 18 × 2 – 20 = 36 – 20 = 16

Thus, length of the side of the square is 16 units.

(i) ↔  (C) (ii) ↔  (E) (iii) ↔  (F) (iv) ↔  (D) (v) ↔  (B) (vi) ↔ (A)

13 subtracted from twice of a number gives 3 .

2x – 13 = 3

Correct answer is 6

If 10 is subtracted from half of a number, the result is 4.

x/2 - 10 =4

Consider the given eqaution, x/2 = 6

x = 6 × 2

x = 12

Then,

= x –

= 12 – (- 3)

= 12 + 3

= 15

x – (-3) = 15; when x/2 = 6

Let the number be x.

So, one third of the number = x/3

On subtracting 1 from it, we get x/3 - 1

x/3 - 1 = 1

x/3 = 1 + 1 = 2

x = 2 x 3 = 6

Thus, x = 6 is the required number.

Consider the given eqaution, 3x = 12

x = 12/3

x = 4

Then,

= x – 0

= 4 – 0

= 4

Consider the given eqaution, 2x = 2

x = 2/2

x = 1

Then,

= x – 1

= 1 – 1

= 0

Let us assume the number be x,

Given, If 5 is added to three times a number = 3x + 5

7 is subtracted from four times the same number = 4x – 7

If 5 is added to three times a number, it becomes the same as 7 is subtracted from four times the same number. This fact can be represented as 3x + 5= 4x – 7.

Consider the given eqaution, x + 7 = 10.

Transpose 7 to RHS then it becomes -7.

x = 10 – 7

x = 3

Consider the given integers, x + 8 = 12 – 4.

x + 8 = 8

Transpose 8 to RHS then it becomes – 8.

x = 8 – 8

x = 0

In natural numbers, x + 8 = 12 – 4 has no solution.

In natural numbers, 4x + 5 = – 7 has No solution.

 In natural numbers, x – 5 = – 5 has No solution.

Consider the given integers, x – 5 = – 5.

Transpose – 5 to RHS then it becomes 5.

x = – 5 + 5

x = 0

In natural numbers, x – 5 = – 5 has no solution.

If 2x + 3 = 5, then value of 3x + 2 is 5

In integers, 4x – 1 = 8 has no solution.

Consider the given integers, 4x + 5 = – 7.

Transpose 5 to RHS then it becomes -5.

4x = – 7 – 5

4x = – 12

x = -12/4 = -3

In natural numbers, 4x + 5 = – 7 has no solution.

it has 1 solution

taking 5 on  LHS to RHS

we get, 4x= -12

therefore x = -3 

Consider the given eqaution, 3x + 10 = 7

Transpose 10 to RHS then it becomes -10.

3x = 7 – 10

3x = -3

x = -3/3

x = -1

x = -1 is the solution of the equation 3x + 10 = 7.

statement. Any value of the variable which makes both sides of an equation equal, is known as a Solution of the equation.

Consider the given integers, 4x – 1 = 8

Transpose -1 to RHS then it becomes 1.

4x = 8 + 1

4x = 9

x = 9/4

In integers, 4x – 1 = 8 has no solution.

4x = 9  (by taking -1 of LHS to RHS)

therefore x = 9/4

Consider the given eqaution, 2x + 3 = 5

Transpose 3 to RHS then it becomes -3.

2x = 5 – 3

2x = 2

x = 2/2

x = 1

then value of 3x + 2 is = (3 × 1) + 2

= 3 + 2

= 5

Consider the given eqaution, 3x – 2 = 7

Transpose -2 to RHS then it becomes 2.

3x = 7 + 2

3x = 9

x =9/3

x =3

x = 3 is the solution of the equation 3x – 2 =7.

Solution

Any value of the variable which makes both sides of an equation equal, is known as a Solution of the equation.

Consider the given equation, (9/5)x = (18/5)

Transpose –x to RHS then it becomes x and – 4 to RHS then it becomes 4,

3 + 4 = x

x = 7

Then, the value of x = 7

(b) transposition

Shifting one term from one side of an equation to another side with a change of sign is known as transposition.

Finding the value of a variable in a linear equation that satisfies the equation is called a root of the equation.

Consider the given equation, (9/5)x = (18/5)

By cross multiplication x = (18/5) × (5/9)

= (18/9)

= 2

Then, the value of x = 2

Any term of an equation may be transposed from one side of the equation to the other side of the equation by changing the sign of the term.