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CHAPTER 1 TOOLS OF
ALGEBRA
1.1 USING VARIABLES
Objective-model relationships with variables, equations, and formulas
DEFINITIONS
• A Variable is a letter that represents an unknown number
• An algebraic expression is a mathematical phrase that includes numbers, variables, and
operation symbols. (NO = sign!)
Some examples:
n+7
x–5
3p
“the sum of t
and 15”
t + 15
“two times a
number x”
2x
“9 less than a
number y”
y-9
“the difference
of a number p
and 3”
p-3
WRITE EACH AS A VERBAL EXPRESSION.
•
𝑦
10
• 19 + x
• 23 – 7
• 6x
18 + y
18 plus y
20x
the product of 20
and x
18 - 15
18 minus 15
7
the quotient of
7 and x
X
the product of a
number and 18
minus 3
the quotient of
25 and x plus
the product of
26 and y
8 less than y
divided by 14
18x – 3
25 + 26y
X
y–8
14
An Algebraic Equation is a mathematical sentence that includes
numbers, variables, an operation symbol, and an equal sign!
Some examples:
n + 7 = 10
x–5=3
3p = 15
An equation has an =
sign and an
expression does not!
A true sentence is a mathematical
sentence that is always correct.
A false sentence is a mathematical
sentence that is incorrect.
An open sentence is a mathematical
sentence that contains one or more
variables.
Examples of True Equations:
2+3=5
6–5=0+1
Examples of Open Equations:
2+x=5
16 – 5 = x + 5
Open equations
have one or more
variables!
IS means = sign
Writing Equations:
“2 more than twice a number is 5”
2 +
2x
= 5
2 + 2x = 5
It can be any letter. We usually see
x and y used as variables.
“a number divided by 3 is 8”
x
or

x 8
3
Sometimes you have to decide
what the variable is…
3 = 8
“the sum of a number and ten is the same as 15”
x + 10 = 15
“The total pay is the number of hours times
6.50”
{Sometimes, two variables are needed}
WRITING AN EQUATION…
Track One Media sells all CDs for $12 each. Write an equation for the total
cost of a given number of CDs.
Define variables and identify key parts of the problem…
WRITING AN EQUATION…
Write an equation to show the total income from selling tickets to a
school play for $5 each.
Define variables and identify key parts of the problem…
WARM UP #1
Write the operation symbol that corresponds to each
phrase.
1. divided by
2. difference 3. more than
4. product
5. minus
6. sum
7. multiplied by 8. quotient
Find each amount.
9. 12 more than 9
10. 8 less than 13
11. 16 divided by 4
12. twice 25
Number of
CDs
Cost
1
$8.50
2
$17.00
3
$25.50
4
$34.00
This table shows the relationship between
number of CDs and cost.
How much is 1 CD?
$8.50
Number of
Cost = $8.50 times (number of CDs)
CDs
Cost
1
$8.50
C = total cost for CDs
2
$17.00
n = number of CDs bought
3
$25.50
4
$34.00
C = 8.50 n
We use a table of values to represent a
relationship.
Number of
hours
Total pay in
dollars
5
40
10
80
15
120
20
160
From the table, we can come up with an
equation.
Total pay = (number of hours) times (hourly pay)
What is the hourly pay?
$8 per hour
Total pay = 8 (number of hours)
T = 8h
WRITE AN EQUATION FOR THE DATA
BELOW…
Gallons
used
4
6
8
10
Miles
Traveled
80
120
160
200