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Objective - To recognize and order integers and to evaluate absolute values.
Integers - The set of positive whole numbers,negative whole numbers, and zero.
{…-3, -2, -1, 0, 1, 2, 3…}
-5 -4 -3 -2 -1 0 1 2 3 4 5
PositiveIntegers
Negative Integers
Origin
Draw a number line and graph the integers.
1) A=6, B= -2, C=5, D=3, E= -4, F=0
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
AB CDE F
2) G=1, H=2, I=4, J= -6, K= -5, L= -2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
LK IHJ G
State an integer that represents the given situation.
1) A gain of 5 yards
2) A loss of 20 gallons
3) A deposit of $342
4) A penalty of 20 points
5) A profit of $38
6) A withdrawal of $12
7) 2 hours before lunch
8) 30 above zero
+5
-20
+342
-20
+38
-12
-2
+30
-5 -4 -3 -2 -1 0 1 2 3 4 5
LargerSmaller
Ordering Integers
Use < or > to compare.
1) -3 4
2) 0 -1
3) -10 -4
4) 6 -8
5) 5 -19
6) -3 -8
7) -9 -2
8) -10 -30
<
<
>
>
>
<
>
>
Place the following integers in order from smallest to greatest.
1) -6, -16, -10, 61, -61
2) -34, -43, 13, -31, -3
3) -5, -9, 9, 15, -59
-61 , -16, -10, -6 , 61
-43 , -34, -31, -3 , 13
-59 , -9 , -5 , 9 , 15
Write the following integers in order from greatest to least.
1) -3, 17, 5, -2, 0, 4
2) -8, -7, 15, -15, -1, 3
3) 40, -4, -400, 4, 14, -41
17, 5 , 4 , 0 , -2
15 , 3 , -1 , -7 , -8
40, 14, 4, -4 , -41
, -3
, -15
, -400
Absolute Value
Absolute Value - The distance a given numberis from zero on the number line.
-5 -4 -3 -2 -1 0 1 2 3 4 5
34
Simplify.
1)
2)
3)
4)
5)
6)
3
4
11
8
19
0
3
4
11
8
19
0
Integer Opposite Absolute Value
7
16
8
33
0
7 7 7
16 16 16
8 8 8
33 33 33
0 0 0
Use < , >, or = to compare.
1)
2)
3)
4)
6)
7)
8)
9)
>
<
=
<
>
<
<
=
5) 10)= >
3
9
3
9
6 6
5 2
7 7
4 2
6 8
3 2
8 8
5 5
Solve.
1)
2)
x 5
x 18
3)
4)
x 3
x 7
x 5 or 5
5, 5
x 18 or 18
18, 18
x 3 1 x 3 1
x 3
No Solution
empty set
null set
t = or -34
Solve each equation below.
1)
2)
3)
4)
5)
6)
x 10
x 4
x 0
x 5
x 14
t 3
4
x = 10 or -10
x = 4 or - 4
x = 0
“no solution”
x = 14 or - 14
34
Determine whether each statement is true always,sometimes, or never for all real numbers.
1)
2)
3)
4)
5)
6)
x x
x x
x x
x 0
x x
x x
sometimes
always
sometimes
never
sometimes
always
Counterexamples
To prove a statement true, it must be proven true for all examples - difficult!
Counterexample - An example that provesa statement false.
Statement: All pets are furry.
Counterexample: Goldfish.
Statement:
Counterexample: x x
x 0
Determine whether each statement is true or falsefor all real numbers. If it is false, find a counter-example that proves it is false.
1)
2)
3)
4)
5)
6)
x 0
x x
x x
x x
x x
x x
False, x = 0
False, x = -7
False, x = -5
True
True
True
