An equation is a condition on a variable such that two expressions in the variable should have equal value.
The value of the variable for which the equation is satisfied is called the solution of the equation.
An equation remains the same if the LHS and the RHS are interchanged.
In case of the balanced equation, if we
Add the same number to both the sides.
Subtract the same number from both the sides.
Multiply both sides by the same number.
Divide both sides by the same number, the balance remains undisturbed, i.e., the value of the LHS remains equal to the value of the RHS
The above property gives a systematic method of solving an equation. We carry out a series of identical mathematical operations on the two sides of the equation in such a way that on one of the sides we get just the variable. The last step is the solution of the equation.
Transposing means moving to the other side. Transposition of a number is similar to adding same number to both sides of the equation or subtracting the same number from both sides of equation.
When a number is transposed from one side of the equation to the other side, we change its sign. For example, transposing +3 from the LHS to the RHS in equation x + 3 = 8 gives x = 8 – 3 = 5.
We can carry out the transposition of an expression in the same way as the transposition of a number.
In an equation, to maintain balance or equality:
Any number added to one side must also be added to other side
Any number subtracted from one side must also be subtracted from other side
Any number multiplied to one side must also be multiplied to other side
Any number divided to one side must also be divided to other side