Definition of the Algebraic Equation
The algebraic equation may be defined as a mathematical statement that has equivalent terms (values) on either side of the equal (=) sign. x + 5 = 10, 3(a + b) = 3a + 3b and 3a B 5 = 10 are all equations, however, the equation 3a B 5 = 10 is a true equation only if a = 5; (3 x 5) B 5 = 15 B 5 = 10; 10 =10. The algebraic number symbols (variables), such as a or b or c . . . x, which are used to represent the unknown numbers are called the unknowns in the equation. The process of finding the value of the unknown in an equation is called solving the equation.

Solving the Equation
Since an equation is a statement of equality, then the left side of the equation must equal the right side. For example, to solve the equation x + 5 = 15, it is necessary to find the unknown variable=s (x) numerical value. This can be done by using one of the four fundamental operations that you learned in Grade 1 arithmetic. Which one?

In this example, we use the operation of subtraction. Why? Because addition and subtraction are opposite operations that undo each other. Addition combines two or more numbers into one larger number and subtraction separates a larger number into two smaller numbers. Hence, in an addition operation, if either addend and the sum are given, for example, as in x + 5 = 15, the other addend (x) can be found by subtracting the addend 5 from the sum 15. Consequently, in an operation of subtraction, if either the minuend or the subtrahend and the difference are given, for example, as in c B 2 = 12, where 2 is the subtrahend and 12 is the difference, the minuend c can be found by adding the subtrahend 2 to the difference 12.

Algebraic equations having only one variable term can be simply solved by changing the sign of the term to an opposite operation, that is, +  to B, B to  +,
to ÷,  ÷ to and transposing the given term to the right side of the equation.