SYMMETRY- ESSENTIAL POINTS
- 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
