Equations and Solutions
What are equations
Any mathematical statement that contains an equal sign is called an equation. The equality sign indicates that the two expressions placed on both sides are equal.
True or false equations
Equations, like any statement in everyday life, may be true or false. For example 3 - 1 = 2 is a true statement, while 3 - 1 = 1 is a false statement.
Conditional equations
An equation that is true for some values of the variable and false for other
values of the variable is called conditional equation.
The equation x + 5 = 6, for example, is neither true or
false. If the variable x is replaced by 1, the equation is a true statement. For
any other number, it is false.
Solutions
A replace value for the variable that make the equation true is called a
solution or root of the equation.
The equation mentioned above has one solution x = 1.
The equation x2 = 4 has two solutions x = 2 or x = -2.
The equation (x - 1)(x - 2)(x - 3) = 0 has three solutions x = 1, 2, 3.
Some equations may have infinite number of solutions. For example, the
equation 2(x + 1) = 2x + 2 is true for every permissible value of x.
Some equations may have no solutions at all. For example, the equation x +
1 =x has no solution. The reason is that any number increased by 1 can not equal
the number itself.