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Systematic (Balancing) Method

In this method, we shall consider a simple equation as a weighing balance. Its two pans are
considered as two sides of the given equation (LHS and RHS) and the equality sign ‘=’ tells us that
both the sides are equal or balanced.

L.H.S. = R.H.S.

To solve an equation using this method, we follow the following rules:

Rules Example Balancing Diagram
Rule I: On adding the same Example: x – 2 = 7
quantity to both sides, the Adding 2 on both sides,
equality of the equation holds x – 2 + 2 = 7 + 2
true. x = 9

x – 2 + 2 = 7 + 2

Rule II: Subtracting the same Example: x + 4 = 7
quantity from both sides, the Subtracting 4 on both sides,
equality of the equation holds x + 4 – 4 = 7 – 4
true. x = 3

x + 4 – 4 = 7 – 4

Rule III: Multiplying both x
sides by the same quantity, the Example: 2 = 6
equality of the equation holds Multiplying both sides by 2,
true. x
× 2 = 6 × 2 x × 2 =
2 2 6 × 2
x = 12

Rule IV: Dividing both sides by Example: 3x = 9
the same quantity, except by Dividing both sides by 3,
0, the equality of the equation 3x 9
holds true. =
3 3 3x 9
x = 3 3 = 3

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