As the name implies constant is a value that remains constant ever. Constant has a fixed value and its value cannot be changed by any variable. Constants are represented by numbers.
For example in the algebraic expression
3x + 5y = 7, where 7 is the constant we know its face value is 7 and it cannot be changed. But 3x and 5y are not constants because the variable x and y can change their value.
A value that keeps on changing is said to be variable. Variables are often represented by an alphabet like a, b, c or x, y, z. Its value changes from time to time.
For example in the algebraic expression:
3x + 5y = 7 where x and y are variables that are changed according to the expression.
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Below is the tabular format of the difference between variable and constant. It will make you more clear what is variable and constant.
From the above table now you have a clear picture of what is the difference in constant and variable.
Now let us solve some examples which will make it more clear what is variable and constant.
Example 1 :
Find the value of x for the equation x - 4 = 0
x - 4 = 0
Add 4 to each side.
X - 4 + 4 = 4
x = 4
So, the value of x is 4.
Example 2 :
Find the value of x for the equation 3x = 27
3x = 27
Divide each side by 3.
3x/3 = 27/3
x = 9
So, the value of x is 9.
Example 3 :
Find the value of x for the equation x + 5 = -2
x + 5 = -2
Subtract 5 from each side.
x + 5 - 5 = -2 -5
x = -7
So, the value of x is -7.
Example 4 :
Find the value of x for equation 4x + 6 = 22.
4x + 6 = 22
Subtract 6 from each side.
4x + 6 - 6 = 22 - 6
4x = 16
Divide each side by 4.
4x/4 = 16/4
x = 4
So, the value of x is 4
So from these problems, we have got different values for the same alphabet x.the values of x keeps on changing depending upon the equation,
So alphabet x is said to be variable.
Find the value of x for the following equation
5x + 10 = 15
7x + 7 = 28
x + 15 = 20
x - 8 = 2
1. What is a Variable? Give an Example.
Answer: A representation of the unknown value is said to be variable. Alphabets like a,b,c …..x,y, z, any of these are used as variables In Mathematics the value of one variable is often dependent on the value of other variables. Even though we have a single value to be found why to use a variable in place of an unknown value the reason is for the equation having more than one variable.
Example 4y = 3x + 2.
Examples of variables are age, income, expenses, etc which does not remain constant are said to be variables.
2. What is the Importance of Variables?
Answer: A variable is any value of any equation that is not fixed it can be changed at any point if time. Variables are so important in computers, science experiments and mathematical equations. It makes the user flexible to work with the equation rather than entering the values directly in the equations. After solving the lengthy equation the variables can be replaced by the real values which makes it quite easy.
3. What is an Algebraic Equation?
Answer: In Mathematics an algebraic expression is a set of integers, variables, constants and mathematical operations like addition subtraction, multiplication, and division that is equated by 0. Both the LHS and RHS are balanced to each other.
Example: 3x + 2y + 3 = 0
Here x and y are variables
3 is constant
The solution of an algebraic equation is the process of finding the number of unknown variables.
For example Consider an equation 2 + 3 = 5
If you want to add 4 to LHS it should be added to RHS too, to balance the equation.
The equation remains balanced if you follow the same procedure every time.