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

Warm up Answers

1.

2.

3.

4.

3 24x

8 28y

7 19x

20 20a b

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