Rules for Rewriting Equations

Consider a weighing balance like the one shown,

Here, Weighing balance is balanced because of "equal weights" on two pans.

Now add a weight of 500 grams in both pans; the weighing balance is still balanced

Similarly remove a weight of 100grams from both pans; weighing balance is still balanced.

We noticed that a weighing balance remains balanced when equal weights are added or removed.

The same thing can be applied to equalities or equations.

Consider an equality which has LHS and RHS as shown.

Now let's add 4 on both sides of the equality, we can see that the equality is still true.

Now subtract 2 on both sides of the equality, we can see that the equality is still true.

Rule 1: If we add the same number on both sides of an equality, it still holds.

Rule 2: If we subtract the same number from both sides of an equality, it still holds.

Now let's multiply 3 on both sides of the equality, we can see that the equality is still true.

Now divide the equality by 4 on both sides, we can see that the equality is true.

Rule 3: If we multiply with the same number on both sides of an equality, the equality still holds.

Rule 4: If we divide an equality by the same number on both sides, the equality still holds.

Rules for Rewriting Equations with Variables.

The discussed rules are also applicable for equations with variables.

Consider an equation where x is a variable as shown.

Adding 5 on both sides of the equation, the equation is still balanced.

Subtracting 8 on both sides of an equation, the equation is still balanced.

Multiplying 4 on both sides of the equation, the equation is still balanced.

Dividing by 4 on both sides, the equation is still balanced.

Revision

If we add, subtract, multiply or divide by the same number on both sides of an equality, the equality still holds.

The End