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A number x divided by 7 gives 2 can be written as (x +1)/7 = 2.

False

False.

One third of a number added to itself = (x/3) + x

One third of a number added to itself gives 10, can be represented as (x/3) + x = 10

One third of a number added to itself gives 10, can be represented as x/3 +10 = x .

False

Let the number be x.

So, one fourth of the number is x/4. 

x/4 is 20 less than the number itself. 

So, the required equation is x/4 = x – 20

m + 3 = 18/4 ⇒ m + 3 = 9/2

(Dividing both sides by 4)

⇒ m = 9/2 – 3

= (9-6)/2 = 3/2

Verification of answer

L.H.S. = 4(m + 3) = 4m + 12

= 4 x 3/2 + 12 (m = 3/2 put )

= 6 + 12 = 18 = RHS

so, m = 3/2 is correct answer.

Let First number = x

Second number = x + 1

Third number = x + 2

Sum of three numbers = 81

∴ According to question,

x + x + 1 + x + 2 = 81

⇒ 3x + 3 = 81

⇒ 3 = 81 – 3, (shifting)

⇒ x = 78/3 = 26

First number = 26

Second number = 26 + 1 = 27

Third number = 26 + 2 = 28

(d) 3

Consider the given equation 7x + 4 = 25

Transpose 4 to right hand side then it becomes –4

7x = 25 – 4

7x = 21

x = 21/7

x = 3

Correct answer is (d) 3

(a) The worth of x coins of Rs 5 each Rs 5x

(b) The worth of x coins of Rs 2 each Rs2x

(c) The equation formed is 5x + 2x = 70

(d) There are10, 5 rupee coins and 10 2 rupee coins.

Let two rupees coins are x in numbers.

So, one rupee coins are 3x in numbers.

According to question, 1(3x) + 2(x) = 120

⇒ 3x + 2x = 120

⇒ 5x = 120

⇒ x = 120/5 24

Thus, 3 × 24 – 72 coins are of one rupee coins.

(a) If 1st prizes are x in number the number of 2nd prizes are 30 – x.

(b) The total value of prizes in terms of x are 2000x + 1000(30 – x)

(c) The equation formed is 1000x + 30000 = 52000

(d) The solution of the equation is x = 22

(e) The number of 1st prizes are 22 and the number of 2nd prizes are 8

Let 1^st prizes are x in numbers.

∴ 2nd prizes are 30 – x in numbers.

According to question,

2000(x) +1000 (30 – x) = 52000

⇒ 2000x + 30000 – 1000x = 52000

⇒ 1000x + 30000 – 52000

⇒ 1000x = 52000 – 30000

⇒ 1000x = 22000

⇒ x = 22000/1000 = 22

∴30 – x = 30 – 22 = 8.

(a) 30

(b) 2000x + 1000(30 – x)

(c) 1000x + 30000 = 52000

(d) x = 22

(e) 22, 8

Answer: If Rahul’s score = x then Sachin’s score = 2x
Then, x + 2x = 200 – 2 = 198
Or, 3x = 198
Or, x = 198 ÷ 3 = 66
Rahul’s score = 66
Sachin’s score = 132

Let Ishu’s age is x years.

Ishu’s father age = 44 years

According to question,

3x + 5 = 44

⇒ 3x = 44 – 5 = 39

⇒ x = 39/3 = 13

So, Ishu’s age 13 year.

Number of road accidents per month in Jaipur = 400

According to question,

Let number of accidents in Jodhpur is x then,

x = 3 x 400 – 50

= 1200 – 50 = 1150

So, number of accidents occured in Jodhpur 1150 per month.

A number is 5 less than 10 times of x then that number is 10x – 5.

Correct answer is 

width = 30 cm, length = 60 cm

Let breadth of the rectangle be x cm.

∴ Length of the rectangle would be 2x cm

∴ Perimeter of the rectangle = 2(2x + x) = 6x

According to question,

x = 60/6 = 10

∴ 2x = 2 × 10 = 20

(a) 2x

(b) 2(2x + x) or 6x

(c) 6x = 60

(d) x = 10

Let the breadth of rectangle be x m.

So, five times of breadth = 5x

Therefore, length of rectangle = (5x – 4) m

Perimeter of rectangle = 40 m

⇒ 2(x + 5x – 4) = 40

⇒ 2(6x – 4) = 40 ⇒ 6x – 4 = 20

⇒ 6x = 20 + 4 = 24

⇒ x = 24/6 = 4

Thus, length of rectangle = (5 × 4 – 4) = 16 m

Correct answer is 6 cm, 12 cm, 12 cm

Let the number be x.

So, seven times of the number = 7x

Thirteen times of the number = 13x

According to question,

7x = 13x – 12

⇒ 12 = 13x – 7x

⇒ 6x = 12

⇒ x = 12/6 = 2

Thus, r -2 is the required number.

Correct answer is 16m

One-fifth of a number is 5 less than that number.

x/5 = x - 5

Correct answer is 50

If 10 less than a number is 65, then the number is 75.

Correct answer is 2 .

Correct answer is (a) 0

Correct answer are 30,42

Let the two numbers be x and y. Then, according to the question, we have

x - y = 12.                                .........(1)

x + y = 72.                                .........(2)

Now, (1) + (2):

x = 30

Substituting the value of x = 30 in (1), we get

y = 42

Hence, 30 and 42 are the two numbers.

Correct answer is 9 years

Mohan is 3 years older than Sohan. The sum of their ages is 43 years.

x = (x + 3) = 43

Correct answer is 11 years, 39 years

Correct answer is 1867

Correct answer is 560

Correct answer is 2

The number is p.

On subtracting 5 from it, we get p – 5

∴ p – 5 = 2 is the required equation.

5 is the solution of the equation 3x + 2 = 17.

True

Correct option is (b) 7x - 1 = 50

We have, x = 7

On multiplying both the sides by 7, we get

7×x=7×7

7x = 49

On adding (-1) both the sides, we get

7x + (-1) = 49 + (-1)

7x - 1= 49 - 1

7x - 1 = 48

Correct answer is (b) 7x – 1 = 50 

12 is a solution of the equation 4x – 5 = 3x + 10.

False

Fill in the blanks to make it a true. 

2x +19 = 11 has the solution – 4.

The root of the equation y – 13 = 9 is 22

Let the amount of money donated by Subramaniam be x.

So, the amount paid by Naidu is= (x + 125)

According to question,

x + x + 125 = 975

⇒ 2x = 975 – 125 = 850

⇒ x = 850/2 = 425

Thus, ₹425 is donated by Subramaniam.

Correct answer is Rs 425

Consider the given equation, (1/6) – x = 1/6

Transpose – x to RHS then it becomes x and 1/6 to LHS then it becomes – 1/6

x = 1/6 – 1/6

x = 0

Then, the value of x = 0

Consider the given equation, x – ½ = – ½

Transpose – ½ to RHS then it becomes ½

x = – ½ + ½

x = 0

Then, the value of x = 0

Consider the given eqaution, x + 15 = 19

Transpose 15 to RHS then it becomes -15.

x = 19 – 15

x = 4

Consider the equation, x – (7/8) = 7/8

Transpose, -7/8 to RHS then it becomes 7/8.

Then, x = (7/8) + (7/8)

x = (14/8) [divide by 2]

x = 7/4

(a) If smaller number is x, the other number is .

From the question it is given that smaller number is x and One is twice the other.

Then, the other number is 2x

(b) The equation formed is .

From the question, smaller number be x, and other number be 2x

Then,

Sum of two numbers is 81,

2x + x = 81

(c) The solution of the equation is .

2x + x = 81

3x = 81

X = 81/3

X = 27

(d) The numbers are and .

x = 27

2x = 2 × 27

= 54

The numbers are 27 and 54.

(a) 20

Consider the given equation (x/2) = 3 to find out the value of x.

x = 3 × 2

x = 6

Then, the value of 3x + 2 will be,

= (3 × 6) + 2

= 18 + 2

= 20

Correct answer is (b) Transposition