# 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**

- If we add same number to both L.H.S and R.H.S of a balanced equation, the equation is still balanced.
- If we subtract same number to both L.H.S and R.H.S of a balanced equation, the equation is still balanced.
- If we multiply same number to both L.H.S and R.H.S of a balanced equation, the equation is still balanced.

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**

Transposing is a value switching side in an equation.

The following rules are to be followed when transposing.

- For number that is added or subtracted, the sign should be changed.
- For number that is multiplied, the number should be divided.
- For number that is divided, the number should be multiplied.

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