 # Linear Equation in One Variable

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• Q1

The sum of two consecutive natural numbers is 25. The numbers are

Marks:1

12 and 13

##### Explanation:

Let two consecutive natural numbers are x and x + 1.
Given, x + (x + 1) = 25

⇒ 2x + 1 = 25

⇒ 2x + 1 – 1 = 25 – 1 (Subtracting 1 from both sides)

⇒ 2x = 24
Hence, x = 12 (Dividing both sides by 2)
and x + 1 = 13

• Q2

There are two numbers, one of them is four times the other. If their sum is 20, then numbers are

Marks:1

4 and 16

##### Explanation:

Let the smaller number be x
So, the bigger number = 4x
Now, x + 4x = 20 (Given)
On solving, we get
5x = 20
⇒ x = 4 (Dividing both sides by 5)
Therefore, smaller number = 4
and bigger number = 16.

• Q3

A number added to 38 gives 45. The number is

Marks:1

7

##### Explanation:

Let the number be x.
Now, x added to 38 gives 45.
i.e., x + 38 = 45

or x + 38 – 38 = 45 – 38 (Subtracting 38 from both sides)
or, x = 45 – 38
or x = 7

• Q4

If 5x + 3 = 18, then the value of x is equal to

Marks:1

3

##### Explanation:

5x + 3 = 18
5x + 3 – 3 = 18 – 3 (Subtracting 3 from both sides)
5x = 15
x = 3 (Dividing both sides by 5)

• Q5

For the given equation 12 + 3(x – 5) = 0, the value of x is

Marks:1

1.

##### Explanation:

12 + 3(x - 5) = 0
⇒12 + 3x - 15 = 0
⇒3x - 3 = 0

⇒3x - 3 + 3 = 0 + 3 (Adding 3 on both sides)
⇒3x = 3
⇒x = 1. (Dividing both sides by 3)