Chapter 4: Simple Equations

Q11Written answer

x exceeds 3 by 7, can be represented as

(a) x + 3 = 2 (b) x + 7 = 3 (c) x – 3 = 7 (d) x – 7 = 3

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Solution:-

(c) x – 3 = 7

Q12Written answer

The equation having 5 as a solution is:

(a) 4x + 1 = 2 (b) 3 – x = 8 (c) x – 5 = 3 (d) 3 + x = 8

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Solution:-

(d) 3 + x = 8

Consider the equation 3 + x = 8.

Transpose 3 to right hand side then it becomes -3

x = 8 – 3

x = 5

Q13Written answer

The equation having – 3 as a solution is:

(a) x + 3 =1 (b) 8 + 2x = 3 (c) 10 + 3x = 1 (d) 2x + 1 = 3

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Solution:-

(c) 10 + 3x = 1

Consider the equation 10 + 3x = 1.

Transpose 10 to right hand side then it becomes -10

3x = 1 – 10

x = -9/3

x = -3

Q14Written answer

Which of the following equations can be formed starting with x = 0?

(a) 2x + 1 = – 1 (b) x/ 2 + 5 = 7

(c) 3x – 1 = – 1 (d) 3x – 1 = 1

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Solution:-

(c) 3x – 1 = – 1

Consider the equation 3x – 1 = – 1.

Transpose -1 to right hand side then it becomes 1

3x = -1 + 1

x = 0/3

x = 0

Q15Written answer

Which of the following equations cannot be formed using the equation x = 7?

(a) 2x + 1 = 15 (b) 7x – 1 = 50

(c) x – 3 = 4 (d) (x/7) – 1 = 0

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Solution:-

(b) 7x – 1 = 50

Consider the equation 7x – 1 = 50.

Transpose -1 to right hand side then it becomes 1.

7x = 50 + 1

7x = 51

x = 51/7

Q16Written answer

If (x/2) = 3, then the value of 3x + 2 is

(a) 20 (b) 11 (c) 13/2 (d) 8

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Solution:-

(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

Q17Written answer

Which of the following numbers satisfy the equation –6 + x = –12 ?

(a) 2 (b) 6 (c) – 6 (d) – 2

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Solution:-

(c) – 6

Consider the given equation –6 + x = –12.

x = -12 + 6

x = -6

Left hand side is equal to Right hand side.

Q18Written answer

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

(a) commutativity (b) transposition

(c) distributivity (d) associativity

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Solution:-

(b) transposition

In Questions 19 to 48, fill in the blanks to make the statements true.

Q19Written answer

The sum of two numbers is 60 and their difference is 30.

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

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Solution:-

From the question it is given that smaller number is x,

Then, the other number is 60 – x

(b) The difference of numbers in term of x is .

Solution:-

From the question, smaller number be x, and other number be (60 – x)

Then,

Difference between the numbers = (60 – x) – x

= 60 – x – x

= 60 – 2x

(c) The equation formed is .

Solution:-

As per the condition given in the question, difference of the two numbers is 30.

So, 60 – 2x = 30

Transpose, -2x to RHS then it becomes 2x and 30 to LHS it becomes -30,

60 – 30 = 2x

30 = 2x

2x – 30 = 0

(d) The solution of the equation is .

Solution:-

30 = 2x

x = 30/2

x = 15

(e) The numbers are and .

Solution:-

x = 15

60 – x = 60 – 15

= 45

The numbers are 15 and 45.

Q20Written answer

Sum of two numbers is 81. One is twice the other.

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

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Solution:-

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 .

Solution:-

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 .

Solution:-

2x + x = 81

3x = 81

x = 81/3

x = 27

(d) The numbers are and .

Solution:-

x = 27

2x = 2 × 27

= 54

The numbers are 27 and 54.

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