Download terms

7.1Variable Notation
In arithmetic, we perform
mathematical operations with
specific numbers. In algebra, we
perform these same basic
operations with numbers and
variables- letters that stand for
unknown quantities.
Algebra is considered to be a
generalization of arithmetic. In
order to do algebra it is important
to know the vocabulary and
notation (symbols) associated
with it.
An algebraic expression consists
of constants , variables , and
operations along with grouping
symbols .
The numerical coefficient of a
variable is the number that is
multiplied by the variable. For
example, the expression 2x +
5 has constants of 2 and 5,
variable of x and x has
coefficient of 2.
The terms of an algebraic
expression are the quantities
that are added (or subtracted).
When a term is the product of a
number and letters or letters alone,
no symbol for multiplication is
normally shown. For example 2x
means 2 times some number x and
abc means some number a times
some number b times some
number c.
Constants are numbers which
do not change in value.
Variables are unknown
quantities and are represented
by letters.
In the expression 2x +3y -5,
the 2, 3, and 5 are constants
and x and y are variables.
To evaluate an algebra
expression, substitute
numbers for the variables and
simplify using the order of
operations. It is a good idea to
replace the variables with their
values in parentheses.
For example to evaluate 2x - y
when x = 5 and y = -3, replace
the variables with their values
in parentheses
2(5) - (-3)
then simplify.
10 + 3 = 13
Terms are always separated by a
plus (or minus) sign not inside
parentheses. The expression
2x - 3y has two terms, 2x and
-3y. 2 and -3 are constants, x
and y are variables with 2 being
the coefficient of x and -3 the
coefficient of y.
The expression 2x +3y -5 has 3
terms.
LIKE TERMS are terms
whose variable factors are the
same. Like terms can be
added or subtracted by adding
(subtracting) the coefficients.
This is sometimes referred to
as combining like terms.
Example: Simplify each
expression by combining like
terms.
• 7y - 2y
• 5w + w
• 5.1x - 3.4x
• 69a - 47a - 51a
• 2x - 6x + 5
• -4y + 8 - y
• -6x - 3 - 5x -4
• 2x + 3y - x +9y
If an algebraic expression that
appears in parentheses cannot
be simplified, then multiply each
term inside the parentheses by
the factor preceding the
parentheses, then combine like
terms.
Example: Simplify the
expression by combining like
terms.
7q  6  4
 7 q  42  4
 7 q  38
Simplify the expression:
2  4 x  3  2
6  4 y  2  7
If an expression inside parentheses
is preceded by a “+” sign, then
remove the parentheses by simply
dropping them. For example:
3x + (4y + z) = 3x + 4y + z
If an expression in
parentheses is preceded by a
“-” sign then it is removed by
changing the sign of each
term inside the parentheses
and dropping the parentheses.
3x – (4y – z) = 3x – 4y + z
Example: Simplify the expression
by combining like terms.
2  (5  8t )
 2  5  8t
 3 8t
An equation is a statement that 2
expressions are equal. The symbol
“=“ is read “is equal to” and divides
the equation into 2 parts, the left
member and the right member. In
the equation
2x + 3 = 13,
2x + 3 is the left member and 13 is
the right member.
The solution to an equation in
one variable is the number
that can be substituted in
place of the variable and
makes the equation true.
For example 5 is a solution to
the equation 2x + 3 = 13
because 2(5) + 3 = 13 is true.
To solve an equation means to find
all solutions or roots for the
equation.
Solve each equation:
• z=4+9
• p = 3(9) – 5
• b = 5(3) – 4(8) + 7
To write a verbal statement into a
symbolic statement:
• Assign a letter to represent the missing
number.
• Identify key words or phrases that imply or
suggest specific mathematical operations.
• Translate words into symbols.
Write the statements into symbols:
• 8 more than a number • 8 + n = 34
is 34.
• 5 less than 3 times a
number is 45.
• The sum of 15, 4 and
a third number is
zero.
• 3x – 5 = 45
• 15 + 4 + t = 0