Equation Weighting balance
In an equation, there is always an equality sign. The equality sign shows that the value of the expression to the left of the sign (the left hand side or LHS) is
In the equation: (4x + 5) = 65, the LHS is (4x + 5) and the RHS is 65. In the equation: (10y – 20) = 50, the LHS is (10y – 20) and the RHS is 50.
If there is some sign other than the equality sign between the LHS and the RHS, it is not an equation.
Thus, 4x + 5 > 65 is not an equation. It says that, the value of (4x + 5) is greater than 65.
Similarly, 4x + 5 < 65 is not an equation. It says that the value of (4x + 5) is smaller than 65.
In equations, we often find that the RHS is just a number. But this need not be always so. The RHS of an equation may be an expression containing the variable.
For example, the equation:
4x + 5 = 6x – 25
has the expression (4x + 5) on the left and (6x – 25) on the right of the equality sign.
Thus,
(1) An equation is a condition on a variable. The condition is that two expressions should have equal value.
(2) Note that at least one of the two expressions must contain the variable.
We also note a simple and useful property of equations. The equation 4x + 5 = 65 is the same as 65 = 4x + 5. Similarly, the equation 6x – 25 = 4x +5 is the same as 4x + 5 = 6x – 25. An equation remains the same, when the expressions on the left and on the right are interchanged. This property is often useful in solving equations.