MATH EQUATIONS - EQUATIONS, TYPES, SOLUTION OR ROOT(S), DOMAIN, LINKS TO OTHERS

Your Ad Here



Please study
Basic Algebra before Math Equations,
if you have not already done so.

There, we introduced the idea of literal number.

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.






Mathematical Statement : Math Equations

Some mathematical sentences are given below.

(i) 8 + 7 = 15. (ii) 9 + 4 > 14 (iii) 16 + 12 < 30 (iv) 3 + 7 ≠ 10

Each of the above sentences can be verified as either true or false.

You can see Sentences (i) and (iii) are true and
Sentences (ii) and (iv) are false.

A Mathematical Sentence that can be verified as either true or falsebut not both is called a Mathematical Statement.

All the four examples given above are Mathematical Statements.











Equality : Math Equations

A true mathematical statement containing the sign ' is equal to' ( = )is called an Equality.

In the above examples, example (i) is an equality.

Great Deals on School & Homeschool Curriculum Books

Open Sentence : Math Equations

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 falsedepending 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

Get The Best Grades With the Least Amount of Effort

Here is a collection of proven tips,
tools and techniques to turn you into
a super-achiever - even if you've never
thought of yourself as a "gifted" student.

The secrets will help you absorb, digest
and remember large chunks of information
quickly and easily so you get the best grades
with the least amount of effort.

If you apply what you read from the above
collection, you can achieve best grades without
giving up your fun, such as TV, surfing the net,
playing video games or going out with friends!

Know more about the

Speed Study System.



Equation : Math Equations

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.

Great deals on School & Homeschool Curriculum Books and Software

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 toits R.H.S. is said to satisfy the equation. A number which thus satisfiesan 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

Solving Equations

Progressive Learning of Math : Math equations

Recently, I have found a series of math curricula
(Both Hard Copy and Digital Copy) developed by a Lady Teacher
who taught everyone from Pre-K students to doctoral students
and who is a Ph.D. in Mathematics Education.

This series is very different and advantageous
over many of the traditional books available.
These give students tools that other books do not.
Other books just give practice.
These teach students “tricks” and new ways to think.

These build a student’s new knowledge of concepts
from their existing knowledge.
These provide many pages of practice that gradually
increases in difficulty and provide constant review.

These also provide teachers and parents with lessons
on how to work with the child on the concepts.

The series is low to reasonably priced and include

Elementary Math curriculum

and

Algebra Curriculum.