Linear Equations in One Variable

Linear equation in one variable is written in the form of ax + b = c, where a, b and c are real numbers with non-zero value of ‘a’.

An algebraic expression is the combination of variables and constants. An equation is a condition on a variable or variables and it is written with an equal sign.

Solution of a linear equation is the value that satisfies the equation. An equation may have linear expressions on both sides.

Variable can be transposed from one side of the equation to the other side.

Constant does not change or vary. The value of a constant is always fixed.

Sometimes an equation has to be simplified before solving it by usual methods.

Some equations that are non linear can be made linear by multiplying both sides of the equation by a suitable expression.

An equation with only one variable having highest power of the variable as 1 is known as linear equation.

The value of the variable that makes an equation true is called a solution of the equation.

The word variable means something that can vary, i.e., change. The value of a variable is not fixed. It can take different values. We may use any letter as a, m, x etc. to show a variable.

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  • Q1

    If 7 – 3(2n – 1) = 4(5 – n) – 7n, then the value of n is

    Marks:1
    Answer:

    2.

    Explanation:
    Given, 7 – 3(2n – 1) = 4(5 – n) – 7n
    Or           7 – 6n + 3 = 20 – 4n – 7n
    Or                       5n = 10
    Or                         n = 2
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  • Q2

    The radius of the Sun is about 695,202 km. If it is about 109 times as big as the radius of the Earth, then the radius of the Earth is

    Marks:1
    Answer:

    6,378 km.

    Explanation:
    Let the radius of Earth = x
    So,        radius of Sun = 109x
                          109x = 695,202       (Given)
                               x = 6,378 km
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  • Q3

    Marks:1
    Answer:

    12.

    Explanation:

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  • Q4

    If the ratio of two numbers is 3 : 4 and their sum is 84, then the numbers are

    Marks:1
    Answer:

    36 and 48.

    Explanation:
    Let a = 3x and b = 4x
    Then, 3x + 4x = 84
    Or       x = 12
    Thus, the numbers are 36 and 48.
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  • Q5

    Two sisters bought books in the ratio 3 : 4. If together they bought 14 books, then the number of books bought by them are

    Marks:1
    Answer:

    6 books and 8 books.

    Explanation:
    Let , the both sister's bought 3x and 4x  books.
    Thus, 3x + 4x = 14
    Or           x = 2 books
    Therefore, number of books bought by them are 6 and 8.
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