An equation is an algebraic statement that two expressions are equal. An equation may be true or false. Truth is determined by evaluating the expressions on either side of the equality '=' symbol. For equations containing variables, the equation may have solutions for some values of these variables. Values of the variables which make an equation true are called solutions of the equation. The set of all solutions to an equation is called a solution set. An identity is an equation that is true for all values of the variables for which it is defined.
Some examples:
Equations which have the same solution set are called equivalent. Examples:2x = 4 is true for x = 2 2x = x + x is an identity
These equations are equivalent since they both have the solution set {2}.2x = 4 x - 2 = 0
These are not equivalent since the first has the solution set {-3, 3} and the second has the solution set {3}.x2 = 9 x = 3
6.1. Solving equations
6.2. Linear equations
6.3. Quadratic equations
6.4. Equations involving radicals
6.5. Solved Problems