We also explained the basic operations like addition,
subtraction, multiplication and division on literal numbers.
We also Explained about Algebraic Expression.
We saw with examples, how to find the value of
an Algebraic Expression by substituting the given
values to the variables involved.
That knowledge is a prerequisite here.
Here, we consider an Algebraic Expression with "=" symbol.
We also discuss the set of values, the variable(s)
can take (replacement set) and the values out of
the replacement set that make the algebraic expression
equal to the R.H.S. of the "=" symbol.
Equation : Math Equations
Before answering the question what is an equation ?
we need to know about certain terminology.
Mathematical Sentence : Math Equations
We have seen that the combination of terms, obtained by the
operation of '+' or '-' or both is called an Algebraic Expression.
If the terms are only numerical (without literals),
the expression is called numerical expression. e.g. 9 + 4, 6 - 3, 15 + 7 - 2, are numerical expressions.
If a numerical expression and a number or
two numerical expressions are joined or connected by
' is equal to' ( = ) or 'is greater than' ( > ) or 'is less than' ( < ) etc,
they are called Mathematical Sentences.
So far we have seen Numerical Expressions joined by
' is equal to' ( = ) or 'is greater than' ( > ) or 'is less than' ( < ) etc,
and called them Mathematical Sentences.
Now consider Sentences in which Algebraic Expressions
with literals (variables) connected by
' is equal to' ( = ) or 'is greater than' ( > ) or 'is less than' ( < ) etc.
What to call them?
The sentences containing variables depend upon the value of the
variable for their truth or falsity.
Such sentences may be true for particular
value(s) of the varaible and false for others.
Such sentences are known as open sentences.
Thus,
A sentence which contains a variable such that it may be true or false
depending on the values of the variable, is called an
Open Sentence.
Some Open Sentences are given below.
(i) x + 3 = 9. (ii) y + 2 > 17 (iii) z - 4 < 5 (iv) p + 8 ≠ 6
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An Open Sentence containing the sign ' is equal to' ( = )
is called an Equation.
In the above examples, example (i) is an equation.
Note that every Equation has two sides, namely
'Left Hand Side' (L.H.S.) and 'Right Hand Side' (R.H.S.).
Thus, in the equation x + 3 = 9, L.H.S. is x + 3 and R.H.S. is 9.
Solution or Root of an Equation : Math Equations
A number which when replaced for the variable of an equation
makes the resulting statement true. i.e., makes its L.H.S. is equal to
its R.H.S. is said to satisfy the equation. A number which thus satisfies
an equation is called a Solution or a Root of the equation.
Solving Equations, Domain of the Variable, Examples
For lucid explanation of the basics of Solving Equations and the concept of Domain of the variable with Examples, and for Links to Solving Linear, Quadratic, Cubic and Bi-Quadratic Equations, go to
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