EQUATIONS –
An algebraic equation represents the quality of two mathematical expressions involving at least one variable (literal). There are some examples are given below -
Example.1) 9 – 3x = 5 Example.2) a² -2a = 10
Example.3) 3x + 4 = 15 Example.4) 7xᶟ + 2x² = 25x – 10
Linear Equations –
A linear equation in one variable, say ‘x’, is an equations in which the exponent of ‘x’ is 1. The general form of a linear equation is ax + b = 0. There are some examples are given below –
Example.1) 2x + 5 = 10 Example.2) 5x – 7 = 15
Example.3) a/3 + 5 = 2a
Solution of an Equation –
The solution or roots of an equation is a number, which when substituted for the variable in the equation makes the left-hand side (LHS) of the equation equal to the right-hand side (RHS). For your better understanding providing some example –
Example.1) The solution of equation a – 3 = 12 is 15 because 15 – 3 = 12
Example.2) 4 is not the solution of the equation 4x + 2 = 3x – 5 because if we substitute or replace the value of x by 4 then we find that => (4 X 4) + 2 = (3 X 4) – 5
Laws Of Equality –
Laws.1) If the same number or quantity is added to or subtracted from both sides of an equation, the two sides remain equal. We can express this symbolically as follows –
If, x = y, then x + k = y + k and x – c = y – c
Laws.2) If both sides of an equation are multiplied or divided by the same non-zero quantity, the sides remain equal.
If, x = y then ax = ay , where a ≠ 0
A B
------------ = ----------- , where y ≠ 0
y y
Transposition –
Any term on one side of an equation can be shifted to the other side by changing the sign of the term. This process is called transposition.
Example.1) If w + x = y – z then w + x – y = - z or w + x – y + z = 0
An equation remains unchanged if all the terms on the LHS are shifted to the RHS and all the terms on RHS are shifted to LHS.