Unit 9 ReviewUnit 9 Review

66thth Grade Grade

Simplify expressions and Simplify expressions and equations with parenthesis.equations with parenthesis.

2(4x+5x)+x=382(4x+5x)+x=38

• X=5X=5

• X=19X=19

• X=2X=2

• I don’t know how to do thisI don’t know how to do this

Great Job!Great Job!

Click here for the next question!

Simplify expressions and Simplify expressions and equations with parenthesis.equations with parenthesis.

• Use the distributive property / order Use the distributive property / order of operations to get rid of of operations to get rid of parenthesisparenthesis

• Use opposites to solve for xUse opposites to solve for x

2(4x+5x)+x=38

38 = (2 * 4x) + (2 * 5x) + x38 = 8x + 10x + x38 = 19x

38 / 19 = 19x / 192 = x

next

Try one on your own…Try one on your own…

(3+4)y + 9 =(3+4)y + 9 =

Check your

answer

(3+4)y + 9 =(3+4)y + 9 =

• 3y + 4y + 93y + 4y + 9

• 7y +97y +9

Remember that the distributive property distributes the operation to everything that is inside the parenthesis!

Click here for the next question!

Apply the Distributive Apply the Distributive PropertyProperty

2y(3+2y)=2y(3+2y)=

• 10y10y

• 6y + (2y)6y + (2y)22

• 5y +4y5y +4y22

• I don’t know how to do thisI don’t know how to do this

Excellent Work!Excellent Work!

Click here for the next question!

Apply the Distributive Apply the Distributive PropertyProperty

• Look up the distributive law by clickinLook up the distributive law by clicking hereg here

• Read the lesson on the distributive prRead the lesson on the distributive property by clicking hereoperty by clicking here

• Try some problems by clicking hereTry some problems by clicking here

Click here for the next question!

Combine Like Terms to Combine Like Terms to Simplify Expressions and Simplify Expressions and EquationsEquations

2y + 6 + 4y – 8 -9y + (-3)=2y + 6 + 4y – 8 -9y + (-3)=

• 3y -53y -5

• 6y – 9y -56y – 9y -5

• -3y -5-3y -5

• I don’t know how to do thisI don’t know how to do this

Incredible!Incredible!

Click here for the next question.

Combine Like Terms to Combine Like Terms to Simplify Expressions and Simplify Expressions and EquationsEquations• Put the things that are alike together!Put the things that are alike together!

2y + 6 + 4y -8 -9y + (-3)2y + 6 + 4y -8 -9y + (-3)

– The variable terms The variable terms 2y, 4y, and 9y2y, 4y, and 9y are one set are one set of termsof terms

– The numbers The numbers 6, 8, and -36, 8, and -3 are a second set of are a second set of like termslike terms

– Each set of like terms is combined separatelyEach set of like terms is combined separately– The variable terms are combined into one The variable terms are combined into one

single termsingle term– The number terms are combined into a second The number terms are combined into a second

single termsingle term2y + 4y – 9y = -3y6 -3 -8 = -5

So, 2y + 6 + 4y -8 -9y + (-3) = -3y - 5

Try one

8b + 9 + 4b – 3b + (-2b) – (-8b + 9 + 4b – 3b + (-2b) – (-5)=5)=

Check your

answer

8b + 9 + 4b – 3b + (-2b) – (-8b + 9 + 4b – 3b + (-2b) – (-5)=5)=

• Like terms are: Like terms are: 8b, 4b, -3b, -2b8b, 4b, -3b, -2b

and: and: 9, -59, -5

• 8b + 4b – 3b + (-2b) = 7b8b + 4b – 3b + (-2b) = 7b

• 9 – (-5) = 149 – (-5) = 14• So, 8b + 9 + 4b – 3b + (-2b) – (-5)= 7b So, 8b + 9 + 4b – 3b + (-2b) – (-5)= 7b

+14+14Click here for more on combining like terms.

Practice combining like terms by clicking here.

Click here for the next question!

Solve EquationsSolve Equations

8y+(-5) = 5y +138y+(-5) = 5y +13

• Y=6Y=6

• Y=-6Y=-6

• Y=18Y=18

• I don’t know how to do this.I don’t know how to do this.

Yes!Yes!

Click here for the next question!

Solve EquationsSolve Equations

• Keep both sides of the equation balanced (be fair)Keep both sides of the equation balanced (be fair)• Get the variable by itselfGet the variable by itself• Follow order of operations (PEMDAS)Follow order of operations (PEMDAS)• Use opposite operations to isolate the variableUse opposite operations to isolate the variable

8y+(-5) = 5y 8y+(-5) = 5y +13+13-5y-5y -5y -5y3y+(-5) = 133y+(-5) = 13-(-5)-(-5) -(-5) -(-5)3y = 183y = 18÷3 ÷3÷3 ÷3Y=6Y=6

Subtract 5y from both sides to combine like termsSubtract -5 from both sides

Divide both sides by 3 to isolate the variable

Try one

4r + 37 = 100 - 5r4r + 37 = 100 - 5r

Check your

answer

4r + 37 = 100 - 5r4r + 37 = 100 - 5r

Add 5r to both sidesAdd 5r to both sides 4r + 37 = 100 – 5r4r + 37 = 100 – 5r

+ 5r + 5r+ 5r + 5r

9r + 37 = 1009r + 37 = 100

Subtract 37 from both Subtract 37 from both sidessides

9r + 37 = 1009r + 37 = 100

- 37 -37- 37 -37

9r = 639r = 63

Divide both sides by 9Divide both sides by 9 r = 7r = 7

Click here to read about solving equations.

Click here to practice solving equations.

Click here for the next question!

Read p. 234 in your student reference book.

Write and identify equivalent Write and identify equivalent expressions and equivalent expressions and equivalent equations. equations.

5(y-b) + 3b – 6y + 4(6 + b)=5(y-b) + 3b – 6y + 4(6 + b)=

• Y + 2b + 24Y + 2b + 24

• -y + 5b – 24-y + 5b – 24

• -y + 2b + 24-y + 2b + 24

• I don’t know how to do this.I don’t know how to do this.

You Got It!You Got It!

Click here for the next question!

Finding Equivalent Expressions Finding Equivalent Expressions and Equationsand Equations

• Think of it like a Think of it like a balancebalance

• If you get stuck, If you get stuck, plug in a number plug in a number for the variablefor the variable

• Make both sides Make both sides equalequal

• Combine like termsCombine like terms

next

Steps to find equivalenceSteps to find equivalence

(12 – 3 + 5k)6 + 4k – 2(k + 5)72 – 18 + 30k + 4k -2k - 10

Use the Use the distributive distributive propertyproperty

72 – 18 – 10 = 4430k + 4k – 2k = 32k

Combine like Combine like termsterms

(12 – 3 + 5k)6 + 4k – 2(k + 5)=44 + 32k(12-3+10)6 + 8 -2(2+5) = 44 + 6419*6 + 8 -2*7 = 44 + 64114 + 8 -14 = 44 + 64108 = 108

Plug in a value to Plug in a value to check (2 = k)check (2 = k)

next

PracticePractice

• Balance the pan balanceBalance the pan balance

Decide if the following are equivalent:

3(4 + 5s) – 12 + (-3s) = 12s yes

2(b + 3) + 4 – (-3b) = -b + 7 no

5(2c + 4) – 3c + (-2)(c+2) = 5c +16 yes

Click here for the next question!

Write and solve equations that Write and solve equations that represent problem situationsrepresent problem situations

When Marlene removed her dinner from the When Marlene removed her dinner from the freezer, the temperature was -10freezer, the temperature was -10°C. She °C. She heated the dinner in the oven, and then heated the dinner in the oven, and then put it on the table. It cooled to room put it on the table. It cooled to room temperature, 23°C while she was talking temperature, 23°C while she was talking on the phone. How many degrees warmer on the phone. How many degrees warmer was the dinner at room temperature than was the dinner at room temperature than when it was removed from the freezer?when it was removed from the freezer?

•10 + x = 23

•23 – 10 =x

•-10 + x = 23

•I don’t know how to do this.

Yahoo!Yahoo!

Click here for the next question!

Write and solve equations that Write and solve equations that represent problem situationsrepresent problem situations

• Identify the important informationIdentify the important information

• Assign a variable to the Assign a variable to the information you do not knowinformation you do not know

• Pay attention to words that would Pay attention to words that would indicate an operation- more than, indicate an operation- more than, in addition, less than, etc.in addition, less than, etc.

• Write a number sentence, solve, Write a number sentence, solve, and checkand check

next

Jenny bought 7 t-shirts, one for each of her Jenny bought 7 t-shirts, one for each of her seven brothers, for $9.95 each. The cashier seven brothers, for $9.95 each. The cashier charged her an additional $13.07 in sales tax. charged her an additional $13.07 in sales tax. She left the store with a measly $7.28. How She left the store with a measly $7.28. How

much money did Jenny start with?much money did Jenny start with? Identify important Identify important informationinformation

7 t-shirts, $9.95 ea7 t-shirts, $9.95 ea

Additional $13.07Additional $13.07

Left with $7.28Left with $7.28

Assign a variableAssign a variable How much money did How much money did she start with = mshe start with = m

Write a number Write a number sentencesentence

M – 7($9.95) -M – 7($9.95) -$13.07= $7.28$13.07= $7.28

Try oneClick here for the next question!

Use Formulas to Solve Use Formulas to Solve ProblemsProblems

15 in

8 in

c

a2 + b2 = c2

• c = √8 + 15

• c = √64 + √225

• c = 64 + 225

• I don’t know how to do this

Great Work!Great Work!

Continue to do math things on portaportal.com

To use formulasTo use formulas

• Substitute the quantities you knowSubstitute the quantities you know

• Solve for the left over variableSolve for the left over variable

V = l x w x h

Vol = 60

5

6

What is the height?

60 = 5 x 6 x h

h = 2

next