Algebra equation

Solving Equations of Algebra: Algebra is a branch of mathematics that is based on the concept of ‘variables’, or unknown values. Solving an equation in Algebra involves a scale, where, the left hand side is equal to the right hand side of the equation. In an algebraic equation, one side consists of the unknown values or the variables, and the other side consists of the known value or number, called ‘constant’.

Placing all the variables and the constants in the appropriate formulae, relevant to the problem, helps in solving a basic algebraic equation. Variables and constants are related to each other with the help of mathematical operations, like:

Multiplication - *
Division - /
Positive or Addition - +
Negative or Subtraction - -
Exponent - ^
Parenthesis or Grouping – ()

For example: Suppose the height of a triangle is 10 cm, and a person is required to find out the base of this triangle, when the area given is 60 sq cm, this is how the problem is solved:

We know, by formula,

Area of a Triangle = ½ * (Base) * (Height)

Since the height of the triangle is known, and is 10 cm, and the area is known too, which is 60 sq cm, but the base of the triangle is not known, so,

Let Base = x (or any letter of the alphabet)
Height = 10 cm
Area = 60 sq cm

Now, placing these values in the formula, we get,

60 sq cm = ½ * (Base) * 10 cm
Which implies,

60 sq cm = ½* x * 10 cm
Or,
60 cm = 5x

Hence, x = 12 cm = Base.

Graphing of Algebraic Equations: Graphical representation of algebraic equations refers to the plotting of all the possible constants of the variables, present in an algebraic equation in a coordinate plane. A simple graphing of algebraic equation requires placing of variables in the coordinates, and marking possible points that denote the absolute value(s) of these variables.

For example: Consider an ‘Absolute Value Function’ of a variable x as 2.

Now,
|x| = 2, means that ‘x’ lies between –2 and 2.

The ‘absolute’ value refers to the concept of a ‘corner’ in the graphing of algebra equations. The corner or a sharp turn appears in the graph, when the variable, x, changes its sign.

Linear Equation of Algebra: A linear equation of algebra involves only the sum of constants, or product of constants, and the first power of a variable. A linear equation of algebra equates a first degree/ linear polynomial to zero. These equations represent straight lines when put in graphs.

Example of a Linear Algebra Equation:

x + y = 3

Linear equations are generally represented in the form, y = mx + b. Here, ‘m’ represents the slope of the straight line, and the constant ‘b’ will determine the point at which this line crosses the y-axis.

It is important to note that any polynomial or rational function is also an algebraic function.

Algebra Equation Calculator: An algebra equation calculator solves an equation by simplifying it, based on the standard order of operations taught in most schools. The calculator takes the value in parenthesis first, followed by the exponent, then multiplication, division, addition and lastly subtraction. There are many free algebra equation solver calculators present on the Internet.

The concept of Algebra is extensively used in solving simple and complex real life problems.