More Equations

Equations can be solved by method of transposing. It is similar to adding or subtracting on both sides.

Transpose simply means - 'how to rearrange an equation'.

It is one of the methods to use in arriving at an answer.

E.g. Consider an equation, 2x + 5 =29

Then to get the value of 'x' we transpose and take 5 away from both sides. Whatever we do to one side of the ‘equal to’ sign, we have to do to the other side also. Therefore

2x + 5 – 5 = 29 - 5

2x = 24

2x ÷ 2 = 24 ÷ 2

X = 12

E.g. Consider an equation, 9n – 4 = 32

9n – 4 + 4 = 32 + 4

9n = 36

9n ÷ 9 = 36 ÷ 9

n = 4

Source: Bhargavi Ramani, 12 June 2013, Text Section, Solving equations by transposing.

Some solution to equation

Equation à Solution (normal path)

Solution à Equation (reverse path)

 Only one solution is found with given solution.

 But with the given solution any number of equations can be formed as explained in formation of equation (I) and (II).

E.g. Let the solution is

           y = 8

Equation- I:

  => 4y = 32

   => 4y-2 = 32 – 2 = 30

Hence equation formed is 4y-2 = 30

Equation- II:

  => 7y = 56

  => 7y + 4 = 56 + 4 = 60

Hence equation formed is 7y + 4 = 60

Equation- III:

  =>3y = 24

  =>3y / 2 = 24 / 2 = 12

Hence equation formed is 3y ÷ 2 = 12

Source: Bhargavi Ramani, 12 June 2013, Text Section, Explains formation of equation from solution.

Topic: Application of simple equations to practical situations

  These equations have wide applications in solving pricing problems, distance/rate problems, work/rate problems, mixing problems, age problems etc.

Solving linear equation is explained in the following video

Solving area of rectangle when perimeter is given is explained in the following video

E.g.: There are two types of boxes containing mangoes. Each box of the larger type contains

4 more mangoes than the number of mangoes contained in 8 boxes of the smaller type.

Each larger box contains 100 mangoes. Find the number of mangoes contained in the smaller box?

Sol: Let number of mangoes in smaller box be ‘m’

     There are 8 smaller boxes =>Total number of mangoes in smaller boxes = 8m

      Each larger box contains 100 mangoes

     Hence from the given condition in problem,

100 = 8m + 4

8m=100-4

8m=96

m=96÷8

m=12.

                Number of mangoes contained in the smaller box = 12

Source: Self (answered a problem from textbook)