Simple EquationsDefinition 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 EquationsInstead 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.
- 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