Linear Equation in One Variable

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  • Q1

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

    Marks:1
    Answer:

    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

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  • Q2

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

    Marks:1
    Answer:

    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.

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  • Q3

    A number added to 38 gives 45. The number is

    Marks:1
    Answer:

    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

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  • Q4

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

    Marks:1
    Answer:

    3

    Explanation:

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

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  • Q5

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

    Marks:1
    Answer:

    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)

     

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