Simple Equations
Equations involving only a linear polynomial are called simple equations.
e.g. 4x + 5 = 65, 10y – 20 = 50
In an equation, there is always an equality sign.
A Simple Equation remains the same when the expression in the left and right are interchanged.
The value of a variable, which makes the equation a true statement is called the solution of a linear equation.
e.g. 5x – 12 = -2 is a equation
L.H.S = 5x – 12 = 5 × 2 – 12 = 10 – 12 = -2
L.H.S = R.H.S
Variables and Expressions
Variable is a quantity that can take any value, its value is not fixed. It is a symbol for a number whose value is unknown yet.
Expressions are formed by performing operations like addition, subtraction, multiplication and division on the variables.
Example: 6x – 3 is an expression in variable x.
Algebraic Equation
An equation is a condition on a variable such that two expressions in the variable should have equal value.
Example: 8x−8=16 is an equation.
The value of the variable in an equation for which the equation is satisfied is called the solution of the equation.
Example: The solution for the equation 2x−3=5 is x=4.
Mathematical Operations on Expressions
- Addition of variables: (3x+4z)+(5y+6)
- Subtraction of variables: (4x−7y)−(6y+5)
- Multiplication of variables: (5xy+6)×7x
- Division of variables: (8xz+5z)/(5x-6y)
