Notes on Equation | Grade 7 > Compulsory Maths > Equation and Inequality | KULLABS.COM

Equation

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Open Statement

source: tutorial.math.lamar.edu Fig: Open statement
source: tutorial.math.lamar.edu
Fig: Open statement

The mathematical statement, which cannot be predicted as true or false statements (until the variable is replaced by any number) are known as an open statement.

x>5, x+3<4, 2y-1≥9 etc. are the example of an open statement.

Linear equations in one variable

source: www.tes.com Fig: Linear Equation in One Variation
source: www.tes.com
Fig: Linear Equation in One Variation

The open statement containing 'equal to' (=) sign and can be true only for a fixed value of variable is called equation.

Further more in x+2 = 5, the equation has only one variable which is x. So, it is the equation of one variable. Also the variable x has power 1.So it is called a linear equation. Thus, x+2 = 5 is a linear equation in one variable.

Solution to equations

Suppose x+2 = 7

This equation can be true only for a fixed value of x which is 5. So, 5 is called the solution (or root) of the equation.The process of getting a solution to an equation. The process of getting a solution to an equation is called solving equation.

Applications of equations

Generally, we use equations to find the unknown value of any quantity. For this, we should consider the unknown value of the given verbal problems as the variable like x, y, a, b etc. Then the verbal problems should be translated into mathematical sentences in the form of equations. And by solving the equations we obtain the required values.



  •  The process of getting a solution to an equation.
  • The process of getting a solution to an equation is called solving equation.

  • The verbal problems should be translated into mathematical sentences in the form of equations.

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Very Short Questions

Solution:

or, 4(3 - x) = 2x - 15
or, 12 - 4x = 2x - 15
or, -4x - 2x = -15 - 12
or, -6x = -27
or, x = \(\frac{27}{6}\)
∴ x = \(\frac{9}{2}\)

Solution:

or, x + 20% of x = Rs 180
or, x + \(\frac{20}{100}\) × x = Rs 180
or, x + \(\frac{x}{5}\)  = Rs 180
or, \(\frac{5x + x}{5}\) = Rs 180
or, \(\frac{6x}{5}\) = rs Rs 180
or, 6x = 5 × Rs 180
or, x = Rs \(\frac{900}{6}\) 
or, x = Rs 150
∴ x = Rs 150

Solution:

Let the other number be x.
Now,
or, x + 21 = 35
or, x = 35 - 21
or, x = 14
So, the required number is 14.

Solution:

Let the smaller part of the sum be Rs x.
Then,
the greater part of the sum = Rs (x + 10) 
Now,
or, x + (x + 10) = Rs 50
or, 2x = Rs (50 - 10)
or, x = Rs \(\frac{40}{2}\)
or, x = Rs 20
∴ The smaller part of the sum = x = Rs 20
The greater part of the sum = Rs (x + 10) = Rs (20 + 10) = Rs 30

0%
  • If x + 4 =  9, then what will be the value of x?

    13
    5
    3
    6
  • If 2x + 1 = x + 3, what will be the value of x?

    1
    2
    3
    4
  • If 3,6x - 6.1 = 5.9 - 2.4x, find the value of x.

    4
    2
    6
    8
  • The sum of two numbers is 28. If one the numbers is 16, find the other number.

    3
    5
    7
    2
  • If x + 20% of x = Rs 180, find the value of x.

    Rs 150
    Rs 120
    Rs 130
    Rs 140
  • Solve: 
    4(3 - x) = 2x - 15

    (frac{3}{2})
    (frac{9}{2})
    (frac{2}{3})
    (frac{2}{9})
  • Solve:
    -(frac{x}{4}) = 5

    -15
    -20
    -5
    -10
  • Solve:

    3(3 - 2x) = -5 (x- 1)

    10
    4
    8
    6
  • The difference of two numbers is 24. If the smaller number is 18, what will be the greater one.

    44
    42
    48
    46
  • Solve:
    x = 220  - 10% of x

    Rs 230
    Rs 220
    Rs 200 
    Rs 210
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