Basic Algebra, also known as Elementary Algebra, deals with the arithmetic operations of unknown variables and natural numbers. Since these variables do not have fixed numerical values, general relationships can be generated to help solve and explore a broader set of problems such as the basic rules of operations.
Consider the following equation:
4x^2 – 3xy + b
x and y are the variables
4 and 3 are the coefficients
2 is the exponent
b is a constant
Algebraic operations work in the same way as normal arithmetic operations. For example, 3xy in the above equation can also be denoted as 3*x*y. With this in mind, arithmetic operations can be used to manipulate algebraic equations. Consider the following equation.
Y + 10xy = 101y
One important rule to remember is that an algebraic equation represents a scale, so an operation done to one side must be done to the other. Thus, for the above equation the following operations can be done:
Divide both sides by y:
1+10x = 101
Subtract 1 from both sides:
Divide both sides by 10
Thus, it can be seen that normal arithmetic operations plays an integral role in the manipulation of algebraic equations. Thus, having a firm grasp and understanding of these rules and principles is crucial for being able to apply algebra for more general problems.© BrainMass Inc. brainmass.com December 8, 2023, 8:37 am ad1c9bdddf