is the equation 3(2x – 4) = (-18) equivalent to 6x – 12 = (-18)?
DESCRIPTION
Is the equation 3(2x – 4) = (-18) equivalent to 6x – 12 = (-18)? Yes, the equations are equivalent by the Associative Property of Multiplication. Yes, the equations are equivalent by the Commutative Property of Multiplication. - PowerPoint PPT PresentationTRANSCRIPT
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CST Algebra 1
Is the equation 3(2x – 4) = (-18) equivalent to 6x – 12 = (-18)?
A. Yes, the equations are equivalent by the Associative Property of Multiplication.
B. Yes, the equations are equivalent by the Commutative Property of Multiplication.
C. Yes, the equations are equivalent by the distributive property of Multiplication over Addition.
D. No, the equations are not equivalent.
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CST Algebra 2
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CST Algebra 3
A. 4B. 6C. 9D. 10
3
316 8
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CST Algebra 4
Which expression is equivalent to
A. C.
B. D.
4
6 2x x
4 3x x5 3x x
7 3x x9 3x x
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CST Algebra 5
Which number does not have a reciprocal?
A. -1
B. 0
C.
D. 3
5
11000
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CST Algebra 6
What is the multiplicative inverse of ?
A. -2
B.
C.
D. 2
6
12
12
12
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CST Algebra 7
What is the solution for this equation?
A. x = -4 or x = 4
B. x = -4 or x = 3
C. x = -1 or x = 4
D. x = -1 or x = 3
7
2 3 5x
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CST Algebra 8
What is the solution set of the inequality
A. -2 ≤ x ≤ 6
B. x ≤ -2 or x ≥ 6
C. -12 ≤ x ≤ 4
D. x ≤ -12 or x ≥ 4
8
5 4 3?x
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CST Algebra 9
Which equation is equivalent to 5x – 2(7x + 1) = 14x ?
A. -9x – 2 = 14x
B. -9x + 1 = 14x
C. -9x + 2 = 14x
D. 12x – 1 = 14x
9 A4.0
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CST Algebra 10
Which equation is equivalent to 4(2 – 5x) = 6 – 3( 1 – 3x)?
A. 8x = 5
B. 8x = 17
C. 29x = 5
D. 29x = 17
10 A4.0
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CST Algebra 11
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CST Algebra 12
The total cost (c) in dollars of renting a sailboat for n days is given by the equation
c = 120 + 60n.If the total cost was $360, for how many days was the sailboat rented?
A. 2B. 4C. 6D. 8
12
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CST Algebra 13
Solve: 3(x + 5) = 2x + 35
Step 1: 3x + 15 = 2x + 35Step 2: 5x + 15 = 35Step 3: 5x = 20Step 4: x = 4
Which is the first incorrect step in the solution shown above?
A. Step 1B. Step 2C. Step 3D. Step 413 A5.0
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CST Algebra 14
A 120-foot-long rope is cut into 3 pieces. The first piece of rope is twice as long as the second piece of rope. The third piece of rope is three times as long as the second piece of rope. What is the length of the longest piece of rope?
A. 20 feetB. 40 feetC. 60 feetD. 80 feet
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CST Algebra 15
The cost to rent a construction crane is $750 per day plus $250 per hour of use. What is the maximum number of hours the crane can be used each day if the rental cost is not to exceed $2500 per day?
A. 2.5 hoursB. 3.7 hoursC. 7.0 hoursD. 13.0 hours
15
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CST Algebra 16
What is the solution to the inequality x – 5 > 14 ?
A. x > 9B. x > 19C. x < 9D. x < 19
16
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CST Algebra 17
The lengths of the sides of a triangle are y, y + 1, and 7 centimeters. If the perimeter is 56 centimeters, what is the value of y?
A. 24B. 25C. 31D. 32
17
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CST Algebra 18
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CST Algebra 19
Which number serves as a counterexample to the statement below?
All positive integers are divisible by 2 or 3.
A. 100B. 57C. 30D. 25
19
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CST Algebra 20
What is the conclusion of the statement in the box below?
If = 4, then x = -2 or x = 2
A. = 4B. x = -2C. x = 2D. x = -2 or x = 2
20
2x
2x
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CST Algebra 21
Which of the following is a valid conclusion to the statement “If a student is a high school band member, then the student is a good musician”?
A. All good musicians are high school band members.
B. A student is a high school band member.
C. All students are good musicians.
D. All high school band members are good musicians.
21
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CST Algebra 22
The chart below shows an expression evaluated for fourdifferent values of x.
Josiah concluded that for all positive values of x,produces a prime number. Which value of x serves as acounterexample to prove Josiah’s conclusion false? A. 5B. 11C. 16D. 2122
X
1 7
2 11
6 47
7 61
2 5x x
2 5x x
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CST Algebra 23
John’s solution to an equation is shown below,Given:Step 1: (x + 2)(x + 3) = 0Step 2: x + 2 = 0 or x + 3 = 0Step 3: x = -2 or x = -3
Which property of real numbers did John use for Step 2?
A. Multiplication property of equalityB. Zero product property of multiplicationC. Commutative property of multiplicationD. Distributive property of multiplication over addition
23
2 5 6 0x x
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CST Algebra 24
Stan’s solution to an equation is shown below,Given: n + 8(n + 20) = 110Step 1: n + 8n + 20 = 110Step 2: 9n + 20 = 110Step 3: 9n = 110 – 20Step 4: 9n = 90Step 5:
Step 6: n = 10Which statement about Stan’s solution is true?
A. Stan’s solution is correct.B. Stan made a mistake in Step 1.C. Stan made a mistake in Step 3.D. Stan made a mistake in Step 5.24
9 909 9n
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CST Algebra 25
When is this statement true?
A. This statement is never true.B. This statement is always true.C. This statement is true for positive numbers.D. This statement is true for negative numbers.
25
The opposite of a number is less than the original number.
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CST Algebra 26
What is the y-intercept of the graph of 4x + 2y = 12
A. -4B. -2C. 6D. 12
26 A6.0
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CST Algebra 27
Which inequality is shown on the graph below?
A.
B.
C.
D.
27
1 12
y x
1 12
y x
1 12
y x
11
2y x
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CST Algebra 28
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CST Algebra 29
A6.0
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CST Algebra 30
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CST Algebra 31
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CST Algebra 32
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CST Algebra 33
What point lies on the line defined by 3x + 6y = 2 ?
A. ( 0, 2 )B. ( 0, 6)C. ( 1, -1/6)D. ( 1, -1/3)
33
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CST Algebra 34
What is the equation of the line that has a slope of 4 and passes through the point (3, -10) ?
A. y = 4x - 22B. y = 4x + 22C. y = 4x - 43D. y = 4x + 43
34 A7.0
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CST Algebra 35
The data in the table shows the cost of renting a bicycle by the hour, including a deposit.
If hours, h, were graphed on the horizontal axis and cost, c, were graphed on the vertical axis, what would be the equation of a line that fits the data?
A. c = 5hB. c = (1/5)h + 5C. c = 5h + 5D. c = 5h – 535
Hours (h) Cost in dollars ( c )2 15
5 30
8 45
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CST Algebra 36
Some ordered pairs for a linear function of x are given in the table below.
Which of the following equations was used to generate the table above?
A. y = 2x + 1B. y = 2x - 1C. y = 3x - 2D. y = 4x - 336
X Y1 1
3 7
5 13
7 19
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CST Algebra 37
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CST Algebra 38
The equation of line l is 6x + 5y = 3, and the equation of line q is 5x – 6y = 0. Which statement about the two lines is true?
A. Lines l and q have the same y-intercept.B. Lines l and q are parallel.C. Lines l and q have the same x-intercept.D. Lines l and q are perpendicular.
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CST Algebra 39
Which equation represents a line that is parallel to
?
A.
B.
C.
D.
39
5 24
y x
5 14
y x
4 25
y x
4 35
y x
5 44
y x
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CST Algebra 40
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CST Algebra 41
What is the solution to this system of equations?
A. ( 6, 2 )
B. ( 1, -5 )
C. no solution
D. infinitely many solutions
41
3 26 2 4y xx y
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CST Algebra 42
Which ordered pair is the solution to the system of equations below?
x + 3y = 7x + 2y = 10
A.
B.
C. ( -2, 3)
D. ( 16, -3 )
42
7 13,2 4
7 17,2 5
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CST Algebra 43
Marcy has a total of 100 dimes and quarters. If the total value of the coins is $14.05, how many quarters does she have?
A. 27
B. 40
C. 56
D. 73
43
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CST Algebra 44
Which of the following best describes the graph of this system of equations?
y = -2x + 35y = -10x + 15
A. two identical lines
B. two parallel lines
C. two lines intersecting in only one point
D. two lines intersecting in only two points44 A9.0
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CST Algebra 45
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CST Algebra 46
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CST Algebra 47
A.
B.
C.
D.
47
3
7
510xx
42x
4
12x
4
15x
4
5x
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CST Algebra 48
A.
B.
C.
D.
48
2 24 2 8 3 2x x x x
23 6x x
23 10x x
23 5 10x x
23 5 6x x
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CST Algebra 49
The sum of two binomials is . If one of the binomials is , what is the other binomial?
A.
B.
C.
D.
49
25 6x x23 2x x
22 4x x
22 8x x
28 4x x
28 8x x
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CST Algebra 50
Which of the following expressions is equal to (x + 2) + (x – 2)(2x + 1)?
A.
B.
C.
D.
50
22 2x x
22 4x x
22x x
24 2x x
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CST Algebra 51
A volleyball court is shaped like a rectangle. It has a width of x meters and a length of 2x meters. Which expression gives the area of the court in square meters?
A. 3x
B.
C.
D.
51
22x
23x
32xA10.0
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CST Algebra 52
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CST Algebra 53
Which is the factored form of
A. (3a – 8b)(a – 6b)
B. (3a – 16b)(a – 3b)
C. 3(a – 4b)(a – 4b)
D. 3(a – 8b)(a – 8b)
53
2 23 24 48a ab b
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CST Algebra 54
Which is a factor of ?
A. x + 3
B. x - 3
C. x + 4
D. x - 4
54
2 11 24x x
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CST Algebra 55
Which of the following shows factored completely?
A.
B. (3t + 4)(3t + 1)
C. (9t + 4)( t + 1)
D.
55
29 12 4t t
23 2t
29 12 4t t
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CST Algebra 56
What is the complete factorization of ?
A. -8(2 + z)(2 – z)
B. 8(2 + z)( 2 – z)
C.
D.
56
232 8z
28(2 )z
28(2 )z
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CST Algebra 57
If is added to x, the sum is 42. Which of the following could be the value of x?
A. -7
B. -6
C. 14
D. 42
57
2x
A14.0
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CST Algebra 58
A14.0
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CST Algebra 59
A14.0
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CST Algebra 60
A14.0
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CST Algebra 61
A14.0
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CST Algebra 62
A14.0
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CST Algebra 63
A19.0
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CST Algebra 64
A19.0
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CST Algebra 65
A20.0
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CST Algebra 66
A20.0
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CST Algebra 67
A20.0
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CST Algebra 68
A20.0
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CST Algebra 69
A21.0
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CST Algebra 70
A21.0
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CST Algebra 71
A21.0
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CST Algebra 72
A21.0
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CST Algebra 73
A22.0
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CST Algebra 74
A23.0
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CST Algebra 75
A23.0
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CST Algebra 76
A23.0
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CST Algebra 77
A12.0
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CST Algebra 78
A12.0
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CST Algebra 79
A12.0
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CST Algebra 80
A12.0
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CST Algebra 81
A12.0
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CST Algebra 82
A13.0
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CST Algebra 83
A13.0
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CST Algebra 84
A13.0
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CST Algebra 85
A13.0
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CST Algebra 86
A15.0
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CST Algebra 87
A15.0
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CST Algebra 88
A15.0
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CST Algebra 89
A15.0
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CST Algebra 90
A15.0
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CST Algebra 91
A15.0
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CST Algebra 92
A16.0
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CST Algebra 93
A16.0
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CST Algebra 94
A17.0
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CST Algebra 95
A17.0
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CST Algebra 96
A18.0