Download Section 6.1анаSolving Equations by Using Inverse Operations

Section 6.1 ­ Solving Equations by Using Inverse Operations
Inverse operations "undo" or reverse each other's results.
Addition is the inverse of subtraction (vise versa)
Multiplication is the inverse of division (vise versa)
We use inverse operations to solve equations
•
•
determine the operation used to build the equation
then use inverse operation to isolate the variable by "undoing" the operations.
One Step Equations...
­
­
­
Start with x
id the operation to produce x + 3
use inverse operation to isolate x
Solve
­ 3
So To verify it is true...
Substitute 6 for x
6 + 3 = 9
1
x 3
Solve
÷ 3
So... n = ­1.2
To verify... 3(­1.2) = ­3.6
­3.6 = ­3.6
ex:
÷ by 4
x by 4
So...
Verify...
Page 271 ­ #5 ­ Class Activity
2
How do we solve these same equations algebraically?
Method 2
Method 1
Note: "What you do to one side
you must do to the other"
Inverse??? Subtraction
Choose which method you like best
ex:
Inverse??? Division
ex:
Inverse??? Multiplication
ex:
Inverse??? Addition
Try these...
3
2 Step Equations
Solve, then verify each equation...
­ 6
Bu
ild
x by 5
÷ by 5
+ 6
Verify...
ex:
+ 3
÷ by 4
­ 3
Bu
ild
x by 4
y = ­3
Verify...
4
+ 3
Bu
ild
÷ by 4
x by 4
­ 3
Verify...
5
ex:
Verify...
Verify...
ex:
Try these...
Text Book: p. 272, #'s 6 ­ 12
Extra Practice #1
6
Using an Equation to Model and Solve a Problem
A rectangle has a length of 3.7cm and a perimeter of 13.2cm. Write an equation that can be used to determine the width.
P = 13.2
w
P = 2L + 2w
13.2 = 2(3.7) + 2w
Solve the equation...
3.7
7
Use an Equation to solve a percent problem
Seven percent of a number is 56.7. Write an equation to solve.
Let n = unknown number
Verify...
Text Book... p. 273, #'s 13 ­ 18, 20, 21
8
Section 6.1
Grade: «grade»
Subject: Mathematics
Date: «date»
9
1 A ­6
B
4
C ­5
D 5
10
2
b ­ 2 = 2
A ­1
B
1
C 0
D 4
11
3 A ­7
B
10
C ­4
D 7
12
4 A ­48
B
­3/4
C 2
D ­14
13
5 A ­7
B
­8
C ­5
D ­6
14
6 A ­9
B
4
C ­8
D 1
15
7 A ­12
B
­8
C 19
D ­6
16
8 A 55
B 16
C D ­6
17
9 A ­54
B
­5
C ­405
D ­36
18
10 A 4
B 13
C 17
D ­24
19
11 Ten years ago, Mary was 58 years old. How old is she now?
20
12 Jill and her best friend found some money buried in a field. They split the money evenly, each getting $8. How much money did they find?
21
13 Brenda had $22 to spend on three notebooks. After buying them she had $16. How much did each notebook cost?
22