Transcript Warm up Lesson 3.3

Warm up Lesson 2.2
Use the distributive property to simplify each expression:
1.
3( x  4)  12
2.
8(a  2b)  4(b  3a)
3.
4( x  7)  3(3  x)
4.
10(2  y )  2(4  y )
Warm up Answers
1.
2.
3x  24
20a  20b
3.
7 x 19
4.
8 y  28
Lesson 2.2
Solving One and Two Step Equations
Strand 1 Concept 2 P.O. 2
Obj: SWBAT
Summarize the properties of and connections between
real number operations; justify manipulations of
expressions using the properties of real number
operations.
Let’s Review….
What is an equation?
An equation is a mathematical statement
that two expressions are equal.
This means, it has an equals sign in it!
Solving Basic Equations
When solving equations, your mission is to get
the variable by itself!
It may start out looking messy, but by the end it
should look something like this:
x = 3, or a = 42, or -16 = m
Inverse Operations…
The most important tool you will learn today and
use when solving equations is inverse operations.
Another word for inverse is opposite!
An inverse operation It is an operation that undoes
a previous operation.
Consider the basic mathematical operations:
addition, subtraction, multiplication, and division.
Each one of these has an inverse…let’s make a
table:
Inverse Operations Table…
Operation
Inverse Operation
Addition
Subtraction
Subtraction
Addition
Multiplication
Division
Division
Multiplication
What does this all mean?
What this means for us now, is that when a number is
being added to a variable, to get rid of it, we must
subtract it. Or if a number is being multiplied by a
variable, we have to divide.
Keep in mind that the equals sign tells us
that whatever we do to one side, we must
do to the other!
Special Property Names:
We refer to these inverse operations using
special properties:
•
•
•
•
The addition property of equality
The subtraction property of equality
The multiplication property of equality
The division property of equality
Practice…
Solve the following for the indicated variable:
2  x  9
y  5  23
x = -11
y = 28
12a  36
a = -3
m
7 
5
m = -35
More Decimals Practice…
2.5x  36.5
x = 14.6
7.382  a  12
a = 4.618
y  21.635  20.52
y = 42.155
m
2.65 
3.24
m = -8.586
What is a reciprocal?
A reciprocal is a multiplicative inverse
which is just a fancy way of saying take a
fraction, flip its top and bottom, and multiply
by that new value!
Given: 2
Its reciprocal is: 3
3
2
Given: 14
1
Its reciprocal is: 
14
1
Given:
7
Its reciprocal is: 7
And still there is more…
Solve the following for the indicated variable:
3
8
x
5
11
x = 40/33 or 1 7/33
5
a 6
8
a = 43/8 or 5 3/8
2 3
y 
7 4
y = 29/28 or 1 1/28
2 3m
 
3
7
m = -14/3 or -4 2/3
Solving 2-step equations
How do we solve
problems such as
Step 1: Isolate the variable by using
the addition or subtraction property
of equality.
Step 2: Combine Like Terms (Simplify)
Step 3: Isolate the variable using
the multiplication or division
property of equality and simplify
3x  15  45
-15
-15
3x  30
3
x  10
3
Let’s check to make sure we did
our work correctly
Start with the original problem
Substitute the variable with
the answer you came up with
remember to put your
answer in ( )
Next, Simplify
3x  15  45
3(10)
x  15  45
30 + 15 = 45
45 = 45
When you have the reflexive property (a
true statement such as this, you should
have done all your work correctly
Let’s try another one
b
 15  25
24
-15
-15
b
 10
24
Let’s see if we did this right: remember start
with the original problem, then use the order
of operations to simplify both sides of the
equal sign.
b
 15  25
24
240
b
24
b
24 
 10  24
24
b  240
 15  25
10 + 15 = 25
25 = 25
What happens when…
we have a problem like
2z  7 z  15  15
Step 1: simplify
5z 15  15
Step 2: Isolate the variable use the
subtraction property of equality
Step 3: Combine Like Terms (simplify)
Step 4: Isolate the numerator by using
the division property of equality
-15
-15
-55z  -530
z 6
Don’t forget to check
Now, You try some on your own be
sure to check your work!
1. 14 x  38  130
w
2.  12   12
4
3.  13  25 y  8
a-12
4.
 42  26
16
1. x  12
2. w  96
1
3. y 
5
4. a  -244
Summary
Explain why inverse operations are
used when solving an equation.
Homework: Worksheet 2.1