8th Grade Notes
The last lesson we completed at school was Lesson 8-2, Solving Two-Step Equations. Let's Review.
To solve any equation that involves a variable the goal is to:
Isolate the variable.
The golden rule of solving equations is:
What you do to one side of the equation you must do to the other.
Solving a Two-Step Equation:
1. Undo the addition or subtraction.
2. Undo the multiplication or division.
Watch the following video and then complete the homework that follows: https://www.youtube.com/watch?v=LDIiYKYvvdA
Lesson 2 Homework Practice
Solving Two-Step Equations
Solve each equation. Check your solutions.
1. 6p + 22 = 10 2. r – 4 = 2 3. 5d – 9 = –24
4. 21q – 11 = –210.5 5. – v + 1 = 0 6. 7h + 20 = –8
7. k – 40 = –26 8. w – 16 = 5 9. s – 5 = 1
10. x + 7 = 9 11. z – 20 = –20 12. – r + 11 = 15
28. A furniture rental store charges a down-payment of $100 and $72.50 per month for a table. Hilde paid $535 to rent the table. Solve 72.50n + 100 = 535 to find the number of months Hilde rented the table.
29. At work, Jack must stuff 1000 envelopes with advertisements. He can stuff 12 envelopes in one minute, and he has 112 envelopes already finished. Solve 1000 = 12n + 112 to find how many minutes it will take Jack to complete the task.
To solve any equation that involves a variable the goal is to:
Isolate the variable.
The golden rule of solving equations is:
What you do to one side of the equation you must do to the other.
Solving a Two-Step Equation:
1. Undo the addition or subtraction.
2. Undo the multiplication or division.
Watch the following video and then complete the homework that follows: https://www.youtube.com/watch?v=LDIiYKYvvdA
Lesson 2 Homework Practice
Solving Two-Step Equations
Solve each equation. Check your solutions.
1. 6p + 22 = 10 2. r – 4 = 2 3. 5d – 9 = –24
4. 21q – 11 = –210.5 5. – v + 1 = 0 6. 7h + 20 = –8
7. k – 40 = –26 8. w – 16 = 5 9. s – 5 = 1
10. x + 7 = 9 11. z – 20 = –20 12. – r + 11 = 15
28. A furniture rental store charges a down-payment of $100 and $72.50 per month for a table. Hilde paid $535 to rent the table. Solve 72.50n + 100 = 535 to find the number of months Hilde rented the table.
29. At work, Jack must stuff 1000 envelopes with advertisements. He can stuff 12 envelopes in one minute, and he has 112 envelopes already finished. Solve 1000 = 12n + 112 to find how many minutes it will take Jack to complete the task.
Tuesday April 7, 2020
Lesson 8-4 More Two-Step Equations
Sometimes Two-Step Equations will include a set of parenthesis. If you encounter a 2-step equation that has a set of parenthesis you should first clear the parenthesis by using the Distributive Property, then complete the 2-step equation.
Watch the following video and then complete the homework that follows: https://www.youtube.com/watch?v=vC9nXIvltjI
Lesson 4 Skills Practice
More Two-Step Equations
Solve each equation.
1. 3(n – 2) = 15 2. 4(x + 2) = 28 3. 56 = 8(p – 5)
4. 36 = 6(y + 2) 12. 6(r + 8) = 20.4
13. 5(g – 10) = 45 15. –3(u + 6) = –27 16. 4(x + 3) = 7
19. 48 = –16(d + 5) 20. 22 = –1(t – 11) 21. 5(j – 12) = 14
Lesson 8-4 More Two-Step Equations
Sometimes Two-Step Equations will include a set of parenthesis. If you encounter a 2-step equation that has a set of parenthesis you should first clear the parenthesis by using the Distributive Property, then complete the 2-step equation.
Watch the following video and then complete the homework that follows: https://www.youtube.com/watch?v=vC9nXIvltjI
Lesson 4 Skills Practice
More Two-Step Equations
Solve each equation.
1. 3(n – 2) = 15 2. 4(x + 2) = 28 3. 56 = 8(p – 5)
4. 36 = 6(y + 2) 12. 6(r + 8) = 20.4
13. 5(g – 10) = 45 15. –3(u + 6) = –27 16. 4(x + 3) = 7
19. 48 = –16(d + 5) 20. 22 = –1(t – 11) 21. 5(j – 12) = 14
Wednesday April 8, 2020
More on Lesson 8-4
Lesson 4 Homework Practice
More Two-Step Equations
Solve each equation.
1. 4(t – 2) = 12 2. 5(y + 3) = 25 3. 45 = 9(x – 5)
4. 42 = 7(p – 13) 5. (h + 6) = 15 6. (s – 1) = 18
7. 24 = (k + 8) 8. (m + 9) = 6 9. 0.3(z – 4) = 15
1 0. 3.4(x – 12) = 13.6 11. (n + 12.6) = 21 12. 5(d – 3) = 17.5
Solve each problem by writing and solving an equation.
22. Tyler is going to the movie theater with two of his friends. In addition to purchasing a ticket, each of them also buys a box of popcorn for $5.50. If the total amount the three friends spent altogether is $41.25, then what is the cost for a movie ticket?
23. Jessica purchases 4 of the same type of scented candles, each of which are on sale for $2 off. After the discount was applied, the total cost for the candles is $19.00. What is the regular price of each candle?
More on Lesson 8-4
Lesson 4 Homework Practice
More Two-Step Equations
Solve each equation.
1. 4(t – 2) = 12 2. 5(y + 3) = 25 3. 45 = 9(x – 5)
4. 42 = 7(p – 13) 5. (h + 6) = 15 6. (s – 1) = 18
7. 24 = (k + 8) 8. (m + 9) = 6 9. 0.3(z – 4) = 15
1 0. 3.4(x – 12) = 13.6 11. (n + 12.6) = 21 12. 5(d – 3) = 17.5
Solve each problem by writing and solving an equation.
22. Tyler is going to the movie theater with two of his friends. In addition to purchasing a ticket, each of them also buys a box of popcorn for $5.50. If the total amount the three friends spent altogether is $41.25, then what is the cost for a movie ticket?
23. Jessica purchases 4 of the same type of scented candles, each of which are on sale for $2 off. After the discount was applied, the total cost for the candles is $19.00. What is the regular price of each candle?
Thursday April 9, 2020
Lesson 8-5 Solving Equations with Variables on Each Side
So now we have variables on each side, what is up with this. Your goal is still the same, Isolate The Variable. The Golden Rule is still the same, What you do to one side of an equation you must do to the other side. Now that you have variables on both sides and constants on both sides you must do some rearranging. I would suggest that until you get better at this, that you always move the variables to the left and the constants to the right. It is what I would do if I were you, but I am not you.
Watch the following video and then complete the homework that follows: https://www.youtube.com/watch?v=f15zA0PhSek&t=428s
Lesson 5 Skills Practice
Solving Equations with Variables on Each Side
Solve each equation. Check your solutions.
1. 3x + 2 = 5x 2. n – 12 = 3n
3. 2 – 3b = 7b + 12 4. d – 11 = d – 6
5. 2f + 3 = 11f – 24 6. 8y + 11 = 2y + 29
7. 5a = –3 + a 8. 17 – 3c = 4c + 3
9. 2a –3 = 9a – 10 10. 5b = 21 + 4b
11. 3(y – 3) = –2y + 6 12. 3n – 5 = 7n
Lesson 8-5 Solving Equations with Variables on Each Side
So now we have variables on each side, what is up with this. Your goal is still the same, Isolate The Variable. The Golden Rule is still the same, What you do to one side of an equation you must do to the other side. Now that you have variables on both sides and constants on both sides you must do some rearranging. I would suggest that until you get better at this, that you always move the variables to the left and the constants to the right. It is what I would do if I were you, but I am not you.
Watch the following video and then complete the homework that follows: https://www.youtube.com/watch?v=f15zA0PhSek&t=428s
Lesson 5 Skills Practice
Solving Equations with Variables on Each Side
Solve each equation. Check your solutions.
1. 3x + 2 = 5x 2. n – 12 = 3n
3. 2 – 3b = 7b + 12 4. d – 11 = d – 6
5. 2f + 3 = 11f – 24 6. 8y + 11 = 2y + 29
7. 5a = –3 + a 8. 17 – 3c = 4c + 3
9. 2a –3 = 9a – 10 10. 5b = 21 + 4b
11. 3(y – 3) = –2y + 6 12. 3n – 5 = 7n
Friday April 10, 2020
More on Lesson 8-5
Lesson 5 Homework Practice
Solving Equations with Variables on Each Side
Solve each equation. Check your solutions.
1. 3g – 12 = 9g 2. 14m = 18 + 12m
3. 7c – 7 = 4c + 17 4. –11t = 15 – 6t
5. 20s + 4 = 13s – 10 6. –2h – 16 = 3(h – 2)
7. 27j – 6 = 14 j + 7 8. –1 + 19w = 11w + 23
9. 8 – p = –12 – 3p 10. 9k – 26 = 6k – 8
11. 4(7 – d) = 5d – 17 12. 2y + 7 = y
Write an equation to find each number. Then solve.
21. Twice a number is 60 more than five times the number. What is the number?
22. Four times a number is 21 more than the number. What is the number?
23. Eight less than three times a number equals the number. What is the number?
24. A number equals six less than four times a number. What is the number?
More on Lesson 8-5
Lesson 5 Homework Practice
Solving Equations with Variables on Each Side
Solve each equation. Check your solutions.
1. 3g – 12 = 9g 2. 14m = 18 + 12m
3. 7c – 7 = 4c + 17 4. –11t = 15 – 6t
5. 20s + 4 = 13s – 10 6. –2h – 16 = 3(h – 2)
7. 27j – 6 = 14 j + 7 8. –1 + 19w = 11w + 23
9. 8 – p = –12 – 3p 10. 9k – 26 = 6k – 8
11. 4(7 – d) = 5d – 17 12. 2y + 7 = y
Write an equation to find each number. Then solve.
21. Twice a number is 60 more than five times the number. What is the number?
22. Four times a number is 21 more than the number. What is the number?
23. Eight less than three times a number equals the number. What is the number?
24. A number equals six less than four times a number. What is the number?
