Types of symbols that are used in algebra: -
In algebra 1 lessons, we come across two types of symbols, namely
Definition of constant: - A symbol which has a fixed numerical value in all situations is known as a constant.
For example: - 5, 30, 246, -7, 5 / 3, 7 / 9, 80.5, -9.6, etc.
Whereas a symbol whose value changes with situation is known as a variable, such as; x, y, p, q, 5x, 7z, etc
Note: - In 3 x, 3 is a constant and x is variable but together 3 x is a variable.
Reason: - As the value of x will change so the value of 3x will also change.
Similarly, 3 is a constant and x is variable but together each of 3 + x, x – 3, x ÷ 3, etc. is a variable.
So, we can say that every combination of a constant and a variable is always a variable.
This combination of constant and variable is known as an expression and the value of the expression depend on the value (s)
of its variable (s).
· 3 + x
· x – 3
· x ÷ 3
Example 1: Solve for x in the equation 5x – 15 = 20
For a given equation if the value of a variable is unknown, then the equation is solved to find the value of the variable.
Different algebraic operations are used in order to solve the given equation.
5x – 15 = 20
Add 15 on both sides of the equation.
5x -15 +15 = 20 + 15
5x = 35
Now, divide by 5 on both sides of the equation.
5x/5 = 35/5;
x = 7
Hence the value of the unknown variable x is 7
Example 2: If x = 0, the value of the expression x – 3
For a given equation, the value can be calculated by plugging the value of variable in the equation
x-3 = 0 – 3 = - 3