The document provides guidance and examples for solving various math problems involving simplifying expressions and equations, combining like terms, using formulas, and writing and solving equations to represent word problems. It includes step-by-step instructions, examples to practice, and checks for understanding.

1. Unit 9 Review 6 th Grade

2. Simplify expressions and equations with parenthesis. 2(4x+5x)+x=38 X=5 X=19 X=2 I don’t know how to do this

3. Great Job! Click here for the next question!

4. Simplify expressions and equations with parenthesis. Use the distributive property / order of operations to get rid of parenthesis Use opposites to solve for x 2(4x+5x)+x=38 38 = (2 * 4x) + (2 * 5x) + x 38 = 8x + 10x + x 38 = 19x 38 / 19 = 19x / 19 2 = x next

5. Try one on your own… (3+4)y + 9 = Check your answer

6. (3+4)y + 9 = 3y + 4y + 9 7y +9 Remember that the distributive property distributes the operation to everything that is inside the parenthesis! Click here for the next question!

7. Apply the Distributive Property 2y(3+2y)= 10y 6y + (2y) 2 5y +4y 2 I don’t know how to do this

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9. Apply the Distributive Property Look up the distributive law by clicking here Read the lesson on the distributive property by clicking here Try some problems by clicking here Click here for the next question!

10. Combine Like Terms to Simplify Expressions and Equations 2y + 6 + 4y – 8 -9y + (-3)= 3y -5 6y – 9y -5 -3y -5 I don’t know how to do this

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12. Combine Like Terms to Simplify Expressions and Equations Put the things that are alike together! 2y + 6 + 4y -8 -9y + (-3) The variable terms 2y, 4y, and 9y are one set of terms The numbers 6, 8, and -3 are a second set of like terms Each set of like terms is combined separately The variable terms are combined into one single term The number terms are combined into a second single term 2y + 4y – 9y = -3y 6 -3 -8 = -5 So, 2y + 6 + 4y -8 -9y + (-3) = -3y - 5 Try one

13. 8b + 9 + 4b – 3b + (-2b) – (-5)= Check your answer

14. 8b + 9 + 4b – 3b + (-2b) – (-5)= Like terms are: 8b, 4b, -3b, -2b and: 9, -5 8b + 4b – 3b + (-2b) = 7b 9 – (-5) = 14 So, 8b + 9 + 4b – 3b + (-2b) – (-5)= 7b +14 Click here for more on combining like terms. Practice combining like terms by clicking here. Click here for the next question!

15. Solve Equations 8y+(-5) = 5y +13 Y=6 Y=-6 Y=18 I don’t know how to do this.

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17. Solve Equations Keep both sides of the equation balanced (be fair) Get the variable by itself Follow order of operations (PEMDAS) Use opposite operations to isolate the variable 8y+(-5) = 5y +13 -5y -5y 3y+(-5) = 13 -(-5) -(-5) 3y = 18 ÷3 ÷3 Y=6 Subtract 5y from both sides to combine like terms Subtract -5 from both sides Divide both sides by 3 to isolate the variable Try one

18. 4r + 37 = 100 - 5r Check your answer

19. 4r + 37 = 100 - 5r 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. r = 7 Divide both sides by 9 9r + 37 = 100 - 37 -37 9r = 63 Subtract 37 from both sides 4r + 37 = 100 – 5r + 5r + 5r 9r + 37 = 100 Add 5r to both sides

20. Write and identify equivalent expressions and equivalent equations. 5(y-b) + 3b – 6y + 4(6 + b)= Y + 2b + 24 -y + 5b – 24 -y + 2b + 24 I don’t know how to do this.

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22. Finding Equivalent Expressions and Equations Think of it like a balance If you get stuck, plug in a number for the variable Make both sides equal Combine like terms next

23. Steps to find equivalence next Plug in a value to check (2 = k) (12 – 3 + 5k)6 + 4k – 2(k + 5)=44 + 32k (12-3+10)6 + 8 -2(2+5) = 44 + 64 19*6 + 8 -2*7 = 44 + 64 114 + 8 -14 = 44 + 64 108 = 108 Combine like terms 72 – 18 – 10 = 44 30k + 4k – 2k = 32k Use the distributive property (12 – 3 + 5k)6 + 4k – 2(k + 5) 72 – 18 + 30k + 4k -2k - 10

24. Practice Balance 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!

25. Write and solve equations that represent problem situations When Marlene removed her dinner from the freezer, the temperature was -10 °C. She heated the dinner in the oven, and then put it on the table. It cooled to room temperature, 23°C while she was talking on the phone. How many degrees warmer was the dinner at room temperature than when it was removed from the freezer? 10 + x = 23 23 – 10 =x -10 + x = 23 I don’t know how to do this.

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27. Write and solve equations that represent problem situations Identify the important information Assign a variable to the information you do not know Pay attention to words that would indicate an operation- more than, in addition, less than, etc. Write a number sentence, solve, and check next

28. Jenny bought 7 t-shirts, one for each of her seven brothers, for $9.95 each. The cashier charged her an additional $13.07 in sales tax. She left the store with a measly $7.28. How much money did Jenny start with? Try one Click here for the next question! M – 7($9.95) -$13.07= $7.28 Write a number sentence How much money did she start with = m Assign a variable 7 t-shirts, $9.95 ea Additional $13.07 Left with $7.28 Identify important information

29. Use Formulas to Solve Problems 15 in 8 in c a 2 + b 2 = c 2 c = √8 + 15 c = √64 + √225 c = 64 + 225 I don’t know how to do this

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31. To use formulas Substitute the quantities you know Solve 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