Chapter 2 Intervention Lesson 2

​Generating Equivalent Expressions

Chapter 2 Intervention Lesson 1

​Additive Inverse

​The Inverse Property of Addition

• Additive Inverses have a sum of zero

• Example:

  • The Additive Inverse of 1 is -1

  • Because 1 + (-1) = 0​

Inverse = Opposite​

• ​Copy this table into your notebook.

• Fill in the center column with the additive inverse.

• ​Show proof that they are opposite.

​

​Don't forget to add this to your table of contents!

​Find the Additive Inverse

​

Fill in the Blank

$$What\ is\ the\ additive\ inverse\ of\ x\ ?$$  

Fill in the Blank

$$What\ is\ the\ additive\ inverse\ of\ -\frac{1}{2\ }?$$  

Fill in the Blank

$$What\ is\ the\ additive\ inverse\ of\ x+3\ ?$$  

Fill in the Blank

$$Subtract\ the\ following\ \exp ression:\ \left(40+9\right)-\left(30+2\right)$$  

Fill in the Blank

$$Subtract\ the\ following\ \exp ression:\ \left(3x+5y-4\right)-\left(4x+11\right)$$  

Fill in the Blank

$$Find\ the\ sum\ of\ the\ \exp ression:\ \left(5a+3b-6c\right)+\left(2a-4b+13c\right)$$  

Fill in the Blank

$$Find\ the\ difference\ of\ the\ \exp ression:\ (2x+3y-4)-(5x+2)$$  

stick = x

string = 4x​

​stick + string = total length

x + 4x = 15

5x = 15

x = 3​

4x = 12

The String is 12 meters long. ​

​Solving Example:

A stick is 𝑥 meters long. A string is 4 times as long as the stick.

• ​Express the length of the string in terms of 𝑥.

• If the total length of the string and the stick is 15 meters long, how long is the string?​

​Word Problem:

​Expressions from Word Problems

Now it's your turn... ​

Fill in the Blank

It costs Margo a processing fee of $3 to rent a storage unit, plus $17 per month to keep her belongings in the unit. Her friend Carissa wants to store a box of her belongings in Margo’s storage unit and tells her that she will pay her $1 toward the processing fee and $3 for every month that she keeps the box in storage. Write an expression in standard form that represents how much Margo will have to pay for the storage unit if Carissa contributes. Then, determine how much Margo will pay if she uses the storage unit for 6 months.

​Multiplicative Inverse

​The Inverse Property of Multiplication

Inverse = Opposite​

• Find the Multiplicative Inverse​

• ​Write out the proof showing the product is 1.

• ​Use the multiplicative inverse to write each expression in standard form (evaluate the expression)

​

​Read through the example!!!

​Multiplicative Inverse: Copy this table into your math notebook!

​

Fill in the Blank

Write the expression in Standard Form (aka evaluate the expression) $$3x+\left(2-4x\right)\ ;\ if\ x=5$$  

Fill in the Blank

Write the expression in Standard Form (aka evaluate the expression) $$3x+\left(-2-4x\right)\ ;\ if\ x=5$$  

Fill in the Blank

Write the expression in Standard Form (aka evaluate the expression) $$3x-\left(-2-4x\right)\ ;\ if\ x=5$$  

Fill in the Blank

Write the expression in Standard Form (aka evaluate the expression) $$3x+\left(-2+4x\right)\ ;\ if\ x=5$$  

Fill in the Blank

Write the expression in Standard Form (aka evaluate the expression) $$3x-\left(2+4x\right)\ ;\ if\ x=5$$  

Fill in the Blank

Write the expression in Standard Form (aka evaluate the expression) $$3x-\left(2-4x\right)\ ;\ if\ x=5$$  

Fill in the Blank

Write the expression in Standard Form (aka evaluate the expression) $$-3x+\left(2+4x\right)\ ;\ if\ x=5$$  

Fill in the Blank

Write the expression in Standard Form (aka evaluate the expression) $$3x-\left(-2+4x\right)\ ;\ if\ x=5$$  

Fill in the Blank

Write the expression in Standard Form (aka evaluate the expression) $$-3x-\left(-2-4x\right)\ ;\ if\ x=5$$  

​Take these Notes...

​Example Problem #1: Two Ways to Solve

4y​ - (3 + y) ; if y = 2

4 (2) - (3 + 2)

4 (2) - (5)

8 - 5

3​

​

Option 1: Order of Operations Option 2: Properties of Addition

4y​ - (3 + y) ; if y = 2

4y - 3 - y

3y - 3​

3 (2) - 3​

6 - 3

3​

​

​Take these Notes...

​Example Problem #2: Two Ways To Solve

Option 1: Order of Operations Option 2: Properties of Addition

(7 + w) - (w + 7)​ ; if w = -4

(7 + (-4)) - (-4 + 7)

(7 - 4) - (-4 + 7)

3 - (3)​

3 - 3

​0

​

(7 + w) - (w + 7)​ ; if w = -4

7 + w - w - 7

w - w + 7 - 7​

0 w​ + 0

0​

​

​

Fill in the Blank

Write each expression in standard form (aka evaluate each expression):

$$\left(2b+1\right)-b\ ;\ if\ b=-4$$  

Fill in the Blank

Write each expression in standard form (aka evaluate each expression):

$$\left(6c-4\right)-\left(c-3\right);\ if\ c=-7$$  

Fill in the Blank

Write each expression in standard form (aka evaluate each expression):

$$\left(d+3d\right)-\left(-d+2\right);\ if\ d=3$$  

Fill in the Blank

Write each expression in standard form (aka evaluate each expression):

$$11f-\left(-2f+2\right);\ if\ f=\frac{1}{2}$$  

Fill in the Blank

Write each expression in standard form (aka evaluate each expression):

$$\left(2g+9h-5\right)-\left(6g-4h+2\right)\ ;\ if\ g=-2,\ h=5$$  

​Example Problem #1:

​Take Notes... 2 Ways to Solve!

When multiplying by a fraction, can divide by the inverse! ​

Fill in the Blank

Write the expression in standard form (evaluate the expression):

$$5\cdot k\cdot-7\ ;\ if\ k=\frac{3}{5}$$  

Fill in the Blank

Write the expression in standard form (evaluate the expression):

$$2\left(-6x\right)\cdot2\ ;\ if\ x=\frac{3}{4}$$  

Fill in the Blank

Write the expression in standard form (evaluate the expression):

$$-3\left(8x\right)+6\left(4x\right)\ ;\ if\ x=2$$  

Fill in the Blank

Write the expression in standard form (evaluate the expression):

$$8\left(5m\right)+6\left(3m\right)\ ;\ if\ m=-2$$  

​Example Problem #1:

​Multiplicative Inverse

​Now your turn to try!

Fill in the Blank

Write the expression in standard form (evaluate the expression):

$$18w\div6\ ;\ if\ w=6\$$  

Fill in the Blank

Write the expression in standard form (evaluate the expression):

$$25r\div5r\ ;\ if\ r=-2\$$  

Fill in the Blank

Write the expression in standard form (evaluate the expression):

$$33y\div11y\ ;\ if\ y=-2\$$  

Fill in the Blank

Write the expression in standard form (evaluate the expression):

$$56k\div2k\ ;\ if\ k=3\$$  

Fill in the Blank

Write the expression in standard form (evaluate the expression):

$$24xy\div6y\ ;\ if\ x=-2,\ y=3$$