Warm up Lesson 2.2
Use the distributive property to simplify each expression:
1.
2.
3.
4.
3( 4) 12x
4( 7) 3(3 )x x
8( 2 ) 4( 3 )a b b a
10(2 ) 2( 4 )y y
Lesson 2.2
Solving One and Two Step Equations
Strand 1 Concept 2 P.O. 2
Obj: SWBATSummarize 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 EquationsWhen 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
Multiplication
Division
Subtraction
Addition
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!
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
Special Property Names:
Practice…
Solve the following for the indicated variable:
2 9x 5 23y
12 36a 75
m
a = -3
y = 28x = -11
m = -35
More Decimals Practice…
2.5 36.5x 21.635 20.52y
7.382 12a 2.653.24
m
a = 4.618
y = 42.155x = 14.6
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: Its reciprocal is:
Given: Its reciprocal is:
Given: Its reciprocal is:
2
3
14
1
7
3
2
7
1
14
And still there is more…Solve the following for the indicated variable:
3 8
5 11x 2 3
7 4y
56
8a 2 3
3 7
m
a = 43/8 or 5 3/8
y = 29/28 or 1 1/28x = 40/33 or 1 7/33
m = -14/3 or -4 2/3
Solving 2-step equationsSolving 2-step equations
45153 xHow do we solve problems such as
Step 1: Isolate the variable by using the addition or subtraction property of equality.
-15 -15
Step 2: Combine Like Terms (Simplify) 303 xStep 3: Isolate the variable using the multiplication or division property of equality and simplify
10x
3 3
Let’s check to make sure we did Let’s check to make sure we did our work correctlyour work correctly
Start with the original problem 45153 xSubstitute the variable with the answer you came up with remember to put your answer in ( )
4515 3 x(10)
Next, Simplify 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 oneLet’s try another one
251524
b
1024
b
-15 -15
241024
24 b
240b
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.
251524
b
251524
b240
10 + 15 = 25 25 = 25
What happens when…
we have a problem like
5 15 15z
2 7 15 15z z
Step 2: Isolate the variable use the subtraction property of equality
5 30z -15 -15
Step 3: Combine Like Terms (simplify)
Step 4: Isolate the numerator by using the division property of equality 6z
Don’t forget to check
Step 1: simplify
-5 -5
Now, You try some on your own be Now, You try some on your own be sure to check your work!sure to check your work!
1. 14 38 130
2. 12 124
3. 13 25 8
a-124. 42 26
16
x
w
y
1. 12
2. 96
13.
54. a -244
x
w
y
Summary
Explain why inverse operations are used when solving an equation.
Homework: Worksheet 2.1