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Simple Equations

Definition of equation: An Equation is condition on a variable such that both sides of the expression should have equal value.
Examples of equation: Consider a variable x.
2x + 5 = 11
3x - 11 = 4

Balanced Equation: An equation whose value is same in L.H.S and R.H.S is a balanced equation.
L.H.S stands for Left Hand Side.
R.H.S stands for Right Hand Side.

Properties of balanced equation

  1. If we add same number to both L.H.S and R.H.S of a balanced equation, the equation is still balanced.
  2. If we subtract same number to both L.H.S and R.H.S of a balanced equation, the equation is still balanced.
  3. If we multiply same number to both L.H.S and R.H.S of a balanced equation, the equation is still balanced.
We can use the above properties to solve equations.
Consider the equation: x + 3 = 11
Now, let us subtract 3 from both L.H.S and R.H.S.
New L.H.S: x + 3 -3 = x
New R.H.S: 11 - 3 = 8
Since, we subtracted similar quantity from both L.H.S and R.H.S, the equation is balanced.
The new equation is: x = 8

Let us look at another equation: 7x = 21.
To solve this equation, let us divide L.H.S and R.H.S with 7.
New L.H.S: 7x / 7 = x.
New R.H.S: 21 / 7 = 3.
The new equation is: x = 3.

Let us see a combination of techniques to solve a more complex equation.
Consider the following equation, where i is variable to solve.
2i/5 + 13 = 33
First let us subtract L.H.S and R.H.S by 13.
New L.H.S = 2i/5 + 13 - 13 = 2i/5
New R.H.S = 33 - 13 = 20
The new equation is: 2i/5 = 20
Next step, let us multiply L.H.S and R.H.S with 5.
New L.H.S: (2i / 5) x 5 = 2i
New R.H.S: 20 x 5 = 100
The new equation is: 2i = 100
Next step, let us divide L.H.S and R.H.S with 2.
New L.H.S: 2i / 2 = i
New R.H.S: 100 / 2 = 50
The final equation is: i = 50

Transposing Equations

Instead of adding or subtracting from both sides of equations, we can use transposing technique to solve equations.
Transposing is a value switching side in an equation.
The following rules are to be followed when transposing.
  1. For number that is added or subtracted, the sign should be changed.
  2. For number that is multiplied, the number should be divided.
  3. For number that is divided, the number should be multiplied.
For example consider the equation:
2x + 5 = 8
Step 1: Transpose 5 from L.H.S to R.H.S, we should change sign.
2x = 8 - 5
2x = 3
Step 2: Transpose 2 from L.H.S to R.H.S, we should convert multiplication to division.
x = 3 / 2

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