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Note: Many problems in this packet will be completed together in class during
review time. Students are not expected to complete every single problem in the
packet. They should complete several problems from each page-- in addition to
studying the notes and past quizzes– in order to be fully prepared for test.
TOPICS COVERED ON “Equations” TEST:
Math Properties
One and Two Step Equations
Multi-Step Equations with Distributive Property
Multi-Step Equations with Combining Like Terms
Multi-Step Equations with Variables on Both Sides
Equation Word Problems
NOTES SPACE/HELPFUL TIPS (to be filled out in class):
Identify the properties used for EACH STEP in order to simplify the following
expressions or equations:
1.
8 + 5 + (-8)
Step 1 = 8 + (-8) + 5
Step 2 = [ 8 + (-8) ] + 5
Step 3 = 0 + 5
Step 4 = 5
_____________________________ Property of Addition
_____________________________ Property of Addition
_____________________________ Property of Addition
_____________________________ Property of Addition
2.
7 + [3(3 + 11)] + 1
Step 1 = 7 + [9 + 33] + 1
_____________________________ Property
Step 2 = 1 + [9 + 33] + 7
_____________________________ Property of Addition
Step 3 = [ 1 + 9] + [ 33 + 7] _____________________________ Property of Addition
Step 4 = 10 + 40
Step 5 = 50
3.
[ (3/4 )(25) (4/3) ] + (-25)
Step 1 = [ (3/4 )(4/3)(25) ] + (-25) _____________________________ Property of Mult.
Step 2 = [ 1(25)] + (-25)
_____________________________ Property of Mult.
Step 3 = [ 25] + (-25)
_____________________________ Property of Mult.
Step 4 = 0
_____________________________ Property of Add.
4.
x(7 + 8) + ( -5 + 5) =
Step 1
7x + 8x + (-5 + 5)= 60
Step 2
7x + 8x + 0 =60
Step 3
(7x + 8x) + 0= 60
Step 4
15x = 60
Step 5
(1/15)15x = 60(1/15)
Step 6
x=4
5.
3y + 6 – 7y - 2 =16
Step 1 3y – 7y + 6 - 2 = 16
Step 2 (3y – 7y) + (6 – 2) =16
Step 3 -4y + 4 = 16
Step 4
-4 -4
Step 5 -4y = 12
Step 6 ( -1/4) -4y = 12 (-1/4)
Step 7
y = -3
__________________________ Property
__________________________ Property of Addition
__________________________ Property of Addition
__________________________ Property of Mult.
_________________________ Property of Addition
________________________ Property of Addition
_________________________Property of Addition
_______________________ Property of Mult.
1. 3x = 21
2. x – 4 = 12
3. 4 + y = -9
4. ½ y = 4
5. -2g = 19
6. -1 = -7 + y
7. 2n – 4 = 18
8. -5y – 3 = -13
9. ¼ y – 1 = 8
10. 5 – 6y = 77
11. 12 = -3z - 6
12. -15 = -92 + 7y
1. 7(10+x) = 84
2. 7(2 + 6x) = 350
3. 3 (-4x – 8) = 108
4. 5(7 – 7x) = 175
5. -2(1 + 4x) = -34
6. -6(5-x) = -78
7. 5(2x -7) = -125
8. -4(10-3x) = 104
9. 7(-2x – 3) = -63
10. 5(-7 + 7x) = 105
11. 6(-8 – 7x) = -468
12. 4(-7 + 7x) = 0
1. 7 – 2x + 6x = 23
2. 16 = 5x + 7x + 4
3. 8 + x + 3x = 36
4. 4x + 5 – 6x = 3
5. 16 = -2x + 5x -8
6. x + 4 + 2x = 19
7. 53 = 3x -2x - 1
8. 5x + 10 – 6x = 15
9. 8 – 2x – 4x = -28
10. -5x + 10 + x = -34
11. 16 = -2 + 5x -8
12. 51 = 6x –x - 4
1. 3x + 8 = -10 + x
2. 6 x+ 9 = 97 – 5x
3. 4x – 9 = -99 – 5x
4. 3x + 9 = 29 + x
5. 7x – 10 = -3x - 120
6. 6x + 3 = 4x + 15
7. 9 – 4x = -7x + 3
8. -3x + 2 = 7 – 4x
9. -5x + 7 = 3x + 31
10. -3 – 6x = 4x -23
11. 4x – 7 = 6x - 17
12. x + 6 = 2x + 12
Write an equation and solve:
1) A large trash can containing 5 tires weighs 13.9 Kg. The trash can, when empty,
weighs 2.2 Kg. How much does one tire weigh? Let “t” represent the weight of
one tire.
2) Barry purchases 8 computers for the same price, and a printer for an additional
$85. If the total bill was $7,919 how much did one computer cost? Let “c”
represent the cost of one computer.
3) A basket full of buttons weighs 2.1 kg. The basket, when empty, weighs 0.24 Kg.
If there are 80 buttons in the basket, how much does one button weigh? Let “b”
represent the weight on one button.
4) Jerry buys 5 baseball bats for the same price, and a batting helmet for $11.50.
If the total bill was $75.95, how much did he pay for one baseball bat?
5) The sum of two consecutive numbers is 43. What is the value of the smallest
number?
6) Amanda decides to split her halloween candy evenly among herself and her
three sisters. After the candy is split up, each sister receives 13 pieces of candy.
How much candy did Amanda have to begin with?
7) For the 7th Grade field trip, Simpson needs 7 school buses. There are 428 total
students going on the field trip– eight will travel by car and the rest will travel
by bus. If each bus will carry the same amount of students, how many students
will be on each bus?
1) Billy purchases 4 value meals for $14.80. Included in the total is $0.84 in sales tax. If “v”
represents the cost of one value meal, which of the following equations represents this
problem?
A
B
C
D
4v + 0.84 = 14.80
4v – 0.84 = 14.80
14.80 + 0.84 = 4v
4 + 0.84 = 14.80v
2) A salesman sells 6 cars in a week and receives a check for $2,650. Included in the check is a
$400 additional bonus. If “c” represents how much he gets paid to sell one car (assume he
gets paid the same for each one), which of the following equations represents this problem?
A
B
C
D
3) Solve for g:
A
B
C
D
400 – 6c = 2650
6c + 400 = 2650
400 + 6 = 2650c
c = 2650
1/
3g
–6=4
g=2
g=6
g = 10
g = 30
4) Which property would you use to justify the following step?
10 + (3x + 5) = 27
10 + (5 + 3x) = 27
A
B
C
D
Inverse Property
Identity Property
Associative Property
Commutative Property
5) Which property would you use to justify the following step?
4x + 2 = 14
-2 -2
A Commutative Property
B Distributive Property
C Inverse Property
D Identity Property
6)
Which property would you use to justify the following step?
3(x -5) = 14
3x – 15 = 14
A
B
C
D
7)
Solve for p: 15 + 7p = 2p
A
B
C
D
8)
5c – 3 = 2c + 6
c=3
c=9
c = -3
c=1
A crate containing 4 boxes of gummy worms weighs 8.4 kg. The crate, when empty, weighs 5.2
kg. Use “g” to represent the weight of one box.
A
B
C
D
10)
p=5
p=3
p = -3
p = -5
What value of c makes this equation true?
A
B
C
D
9)
Associative Property
Identity Property
Commutative Property
Distributive Property
4(g + 8.4) = 5.2
4g + 5.2 = 8.4
4g = 8.4
5.2 + 8.4 = 4g
Jack splits his allowance money evenly between himself and his brother. Then, his grandfather
gives him an additional $20. If Jack ends up with $50, how much did he originally have in
allowance money (before he split it with his brother)? Set up an equation and solve.
A
B
C
D.
x = 25
x = 35
x = 60
x = 100