Transcript 1-4 Equations and Inequalities

2-2 HW = Pg. 75-77 #12-32e, 33-38, 44-50e, 62-78e
2-2 HW Continued
2-3 Subtraction of Real Numbers
1.) Subtraction can be turned into addition
-
adding the opposite of the second number is
equivalent to subtracting the number
2.) Rules
-
a - b = a + (-b)
Ex: 3 - 5 = 3 + (-5) = -2
Terms = parts of an expression that are
separated by addition or subtraction signs
- Ex: -9-2x has 2 terms, 4 y  7 x  9 has 3 terms
2
Important Rules to follow with Addition, DO NOT
work for subtraction!
• Commutative Property
a b  b  a
5-4  4-5
• Associative Property
a  (b  c)  (a  b)  c
8-(7-6)  (8-7)-6
• Property of Zero (Inverse Property)
a  (a)  0
a-(-a) = a+a=2a
8-(-8)=8+8=16
This property STILL works for subtraction
• Identity Property
a –0=a
Practice
Use the subtraction rule to rewrite the
subtraction expression as an equivalent
addition expression. Then evaluate the
expression.
Answers :
1.)4  5  4  (5)  1
• 1.) 4-5
2.)3  (8)  3  (8)  11
• 2.) 3-(-8)
3.)0  7  0  (7)  7
• 3.) 0-7
4.)2  ( 3)  2  (3)  5
2
1 1
2
1
1
• 4.) 2-(-3)-6
5.)   ( )     ( )  ( )
3
6 3
3
6
3
2
1 1
• 5.)   ( ) 
4 1
2
5
3
6
3
    ( )  
6 6
6
6
Practice 2
Evaluate the expression
1.) 8-11-(-6)
2.) 3-(-8)+(-9) 3.) –7+42-63
4 2
5
4.) 6-1+10-(-8)
5.)    ( )
9
3
6
Find the terms of the expression
6.) -4-y
7.) -3x+6
8.) x-y-7
Evaluate the function for these values of x: -2, -1,
0, and 1. Organize your results in a table
9.) y = x - 8
10.) y = -x + 12
Practice 2 - Answers
1.) 8-11-(-6) = 8+(-11)+(+6) = 3
2.) 3-(-8)+(-9) = 3+(+8)+(-9) = 2
3.) –7+42-63= -7+42+(-63) = -28
4.) 6-1+10-(-8) = 6+(-1)+10+(+8) = 23
4 2
5
8
12
15
-35
17
5.)  9  3  ( 6 ) = - 18  ( 18 )  ( 18 ) = 18  118
6.) -4-y : 2 terms –4 and y
7.) -3x+6 : 2 terms –3x and 6
8.) x-y-7 : 3 terms x, -y and -7
9.) X -2 -1 0 1 10.) X -2 -1 0
Y
-10 -9
-8
-7
Y
1
14 13 12 11
When will
I ever use
this?
Summary
• Adding the ___________ of a number is
equivalent to subtracting the number.
• The following properties DO NOT work for
subtraction _______________,
_______________, and _______________.
• The ___________ ______________ is the only
addition property that works for subtraction.
• The parts in a expression separated by addition
symbols are called___________.
Check Yourself
Pg. 82-85 #16-70 eoe, Quiz 1 #1-20 and study
for Ch.2 Quiz 1
• # 16-34: find the difference by changing
subtraction to addition of the opposite
• #36-50: evaluate the expression by
substituting first
• #52-58: find the terms and list them
• #60-70: evaluate the expression