QUESTION 4

SOLUTION

Let the number be x,

ACCORDING to the question,

⇒ Number + Half of the Number = 30

⇒ x + x/2 = 30

⇒ (2x + x)/2 = 30

⇒ 3x = 60

⇒ x = 20

Hence, The given number is 20.

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QUESTION 5

SOLUTION

Given, ax = b is a equation where a and b are positive integers will always be a positive integer.

Because, In the given linear equation, We see that the numbers on both sides must be positive, because a negative number (ax) can't be equal to a positive number (b)

So, In order to make the condition remain true, x must be positive.

Hence, the solution will be a positive number.

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QUESTION 6

SOLUTION

The first and the last linear equation have negative integer and negative fraction as its solution respectively.

Since,

• 2x + 6 = 0

⇒ 2x = -6

⇒ x = -3 ( A negative integer)

• 4X + 7 = x + 2

⇒ 4x - x = 2 - 7

⇒ 3x = -5

⇒ x = -5/3 ( A negative fraction )

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QUESTION 7

SOLUTION

• 4x + 1 = 2

⇒ 4x = 2 - 1

⇒ 4x = 1

⇒ x = 1/4

∵ 1/4 ≠ 5 , So this is not the answer.

• 3 - x = 8

⇒ -x = 8 - 3

⇒ -x = 5

⇒ x = -5

∵ Again, -5 ≠ 5, Again this option is neglected.

• x - 5 = 3

⇒ x = 8

∵ Again, 8 ≠ 5, This option is also neglected.

• 3 + x = 8

⇒ x = 8 - 3

⇒ x = 5

∵ Here, x = 5, So this is the right answer.

Hence, Option D is the correct answer.

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QUESTION 8

SOLUTION

Option B is the correct answer.

⇒ x = 7

Multiply both sides by 7

⇒ 7x = 49

Subtract 1 both sides

⇒ 7x - 1 = 49 - 1

⇒ 7x - 1 = 48

Here, It is given as 7x - 1 = 50 , which must be 7x - 1 = 48

Hence, Option B is the correct answer.