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ter 1: Introduction to Algebra
Chapter 1: Introduction to Algebra

Algebra is a branch of mathematics
that deals with variables, numbers,
and the operations that can be
performed on them
...
This
chapter serves as an introduction to
the basic concepts of algebra
...
1 What is Algebra?

At its core, algebra is the study of
mathematical symbols and the rules
for manipulating these symbols
...
This
allows us to solve problems and
make general statements about
numbers that are true for all values
of the variables
...
These
unknowns are represented by
symbols, usually letters, which stand
for numbers we do not know yet
...

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1
...
Variables:
Variables are symbols (often letters
like x, y, z) that represent numbers
...
The value
of a variable is not fixed and can
change depending on the situation
...


2
...
In the expression 2x + 3,
the number 3 is a constant, while x
is a variable
...
Expressions:
An algebraic expression is a
combination of variables, constants,
and operations (addition,
subtraction, multiplication, division)
...


4
...
It contains an equals sign (=)
and shows the relationship between
two expressions
...


5
...
In the equation x + 3 =
7, the solution is x = 4, because
when x = 4, the equation becomes 4
+ 3 = 7, which is true
...
3 Basic Operations in Algebra

In algebra, we perform the same
basic operations as in arithmetic:
addition, subtraction, multiplication,
and division
...


1
...

Example: 3x + 2x = 5x (combining
like terms)
...
Multiplication:
Multiplying variables involves the
distributive property, where you
multiply the coefficient (the number
in front of the variable) by the
variable
...


3
...

Example: 6x ÷ 2 = 3x
...
4 The Language of Algebra

Algebra uses a special language
that helps in understanding
relationships and solving problems
...
For example, 3x, 5, and -2xy
are terms
...
In 3x, the
number 3 is the coefficient of x
...
In 3x + 5, the
number 5 is the constant
...
For example, 3x and 7x are
like terms because they both contain
the variable x
...
5 Evaluating Algebraic Expressions

To evaluate an algebraic expression,
substitute the values of the variables
into the expression and simplify
...


Substitute the values: 3(2) + 2(4) = 6
+ 8 = 14
...
6 Writing Algebraic Expressions

An algebraic expression can
represent a real-world problem
...


Example:
"Five more than twice a number" can
be written as 2x + 5, where x is the
unknown number
...
7 Solving Simple Equations

The goal of algebra is often to solve
equations—find the value of the
variable that makes the equation
true
...
Isolate the variable on one side of
the equation by using inverse
operations (addition, subtraction,
multiplication, division)
...
Simplify the equation
...
Check the solution by substituting
it back into the original equation
...
Subtract 3 from both sides: x = 7 3
...
Simplify: x = 4
...
Check: Substitute x = 4 into the
original equation: 4 + 3 = 7
...

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1
...
It
helps us understand relationships,
patterns, and structures that we
encounter every day
...
9 Summary

In this chapter, we have introduced
the basic concepts of algebra,
including variables, constants,
expressions, and equations
...
This
knowledge is foundational to solving
more complex algebraic problems
and will be built upon in subsequent
chapters
...

The key to success in algebra is
practice—so be sure to work through
problems regularly to master the
concepts

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