Okay, let's break this down step-by-step: * The population is dropping at a rate of 255 people per year * We want to know how long it will take for the change in population to be 2,040 people * So we set up an equation: Rate x Time = Change * Rate is -255 people/year * Change is -2,040 people * So the equation is: -255x = -2,040 * Solve for x: x = 2,040/-255 = 8 years Therefore, it will take 8 years for the change in population to be 2,040 people.

1. • 1. Review: Prime Factorization, Solving One-
Step Equations
• 2. Objectives for 2.1

3. 1. Define the set of integers.
The collection of positive whole numbers, the negatives
of the whole numbers, and 0 is called the set of integers.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

4. The Number Line
 Algebra uses
NEGATIVE and
-5 -4 -3 -2 -1 0 1 2 3 4 5
POSITIVE numbers.
The numbers in
 Algebra also uses Algebra uses all of red are the
the numbers on numbers we have
variables, or letters the number line, worked with so far.
both positive and
to represent the negative.
unknown values.

5. 2. Graph integers on the number line.
To graph a number means to make a drawing that
represents the number.
Graph -4,
-2, 0, and
3 on a -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
number
line.

6. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
• The arrows at both ends of the number line mean that the positive and negative
numbers go on forever.
ZERO is neither
•Positive numbers are to the right of zero.
positive nor negative.
•Negative numbers are to the left of zero.
•A number on the number line is greater than any number to its left.
•A number on the number line is less than any number to its right.

7.  Positive numbers do not have to be written
with a plus sign.
 Positive 8 is simply written as 8.
 Negative numbers MUST be written with a
negative sign in front of them (-8)

8. I
H A G C D E F J B
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
1. +6 J 5. 1 F 9. -5 C
2. -3 D 10. 4
I
6. -6 G
3. 9 B
4. -8 7. 0 E
A
8. - 9 H

9. 3. Use inequality symbols to compare
integers.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

10. 3. Use inequality symbols to compare
integers.
false false
true false

11. 4. Find the absolute value of an integer.
 Absolute Value is the distance from a number
to zero on the number line.
 Absolute Value is neither positive or negative.
 The absolute value of -5 is 5 .
 What is the absolute value of -7?

12. 5. Find the opposite of an integer.
The opposite of negative 5 is positive 5.

13.  Assignment 1 is due tomorrow and it would
be a great use of you time to “get ‘er done”. If
you’ve already finished, try working ahead on
assignment #2.

14.  Adding Two SAME-Signed Numbers:
 Add and give the total of the signed
numbers.
 (-5) + (-5) = -10
 5 + 5 = 10
 (-3) + (-2) = -5

15.  Adding when the signs are different:
 Subtract and keep the sign of the bigger number.
 8 + (-15)
 Subtract :
 15-8 =7
 The sign of the larger number is negative
 So, the answer is -7

16.  Simplify (-9) + (10) + (-8) + (4) =
 Step 1: Add the positive numbers.
 Step 2: Add the negative numbers.
 Step 3: Add sums together.

17.  If you get confused, try not to get wrapped up
in the WHY of all the rules.
 Sometimes some rules don’t make sense, but
we accept that we must follow them anyway.
 You’ve been warned!

18.  Change the minus to plus and change the
sign of the number on the right ONLY.
Different Signs (-8) - (3)= -11
Same Signs
(-8) - (-3)= -5

19.  To subtract signed
numbers:
 Step 1: Change
the sign of the
number being
subtracted. -8
 Step 2: Follow the
signs for adding
signed numbers.

20.  This is where it gets weird.
 Step 1: To solve a series of Same
signed numbers, start by
changing the signs of
numbers being subtracted.
 Step 2: Find the sum of the
positive numbers.
6 + 4 = 10
 Step 3: Find the sum of the -2+ (-5) = -7
negative numbers.
 Step 4: Find the difference. 10- 7 = 3
Follow the rules of addition.

21.  Subtraction:
 Add the
opposite
 Addition:
 Different
signs, subtract
and keep the
sign of the
larger number
 Same signs,
add and keep
the sign

22. 1. -4
2. -2
3. 2
4. 4
Answer Now

23. 1. -9
2. -3
3. 3
4. 9
Answer Now

24. 1. 12 + 3
2. -12 + 3
3. -12 - 3
4. 12 - 3
Answer Now

25. 1. -9
2. -5
3. 5
4. 9
Answer Now

27. A negative times a negative is a A negative times a positive is a
positive. negative.

28.  If you gain 2 pounds a
week for 5 weeks, you will (+2)(+5) = +10
weigh 10 pounds more
than you weigh now.  Step 1: Multiply.
 Step 2: If same signs, make the
product positive.
 If you lose 2 pounds a  Step 3: If different signs, make the
week for 5 weeks, you will product negative.
weigh 10 pounds less than
you weigh now.
(-2)(+5) = -10

29.  If you have been gaining 2
pounds a week for 5 weeks, (+2)(-5) = -10
you weighed 10 pounds less
five weeks ago.  Step 1: Multiply.
 Step 2: If same signs, make the
product positive.
 Step 3: If different signs, make the
 If you have been losing 2 product negative.
pounds a week for 5 weeks,
you weighed 10 pounds
more 5 weeks ago. (-2)(-5) = +10

30.  What is (-6)(+2)(-4)? 48
 Rule:
 Step 1: Multiply.
 Step 2: If there are even negative signs, the final
product is POSITIVE.
 Step 2: If there are an odd number of negative
signs, the final product is NEGATIVE.

31.  Step 1: Multiply.
 Step 2: If same signs, make the product
positive.
 Step 3: If different signs, make the
product negative.

32.  The rule for dividing
is similar to the rules -5
for multiplying.
 Same signs = positive
 Different signs =
negative

33.  The population of a small town is dropping at
a rate of 255 people per year. How long will it
take for the change in population to be 2,040
people?