Question

1.
What is the value of x in the equation –6 + x = –3? (5 points)


–9
–3
3
9
2.
How many solutions does the equation –2a + 2a + 7 = 8 have? (5 points)


One
Two
None
Infinitely many
3.
What is the value of y in the equation 2(2y – 16) = 0? (5 points)


4
6
8
9
4.
How many solutions does the equation 5p – 4p – 8 = –2 + 3 have? (5 points)


One
Two
None
Infinitely many
5.
The steps below show the incomplete solution to find the value of n for the equation 4n – 2n + 4 = –1 + 17:

Step 1: 4n – 2n + 4 = –1 + 17

Step 2: 4n – 2n + 4 = 16

Step 3: 2n + 4 = 16

Which of these is most likely the next step? (5 points)


2n = 12
2n = 4
2n = 8
2n = 20
6.
What is the value of z in the equation 2(4z – 3 – 1) = 166 – 46? (5 points)


14
15
16
17
7.
What is the value of x in the equation –x = 3 – 4x + 6? (5 points)


–9
–3
3
9
8.
How many solutions does the equation 4n + 6 = 4 + 2 + 4n have? (5 points)


Two
Many
None
One
9.
Which of these is a simplified form of the equation 6y + 4 = 8 + 2y + 2y? (5 points)


6y = 8
10y = 12
2y = 4
4y = 12
10.
The work of a student to solve the equation 3(2x – 4) = 8 + 2x + 6 is shown below:

Step 1: 3(2x – 4) = 8 + 2x + 6

Step 2: 5x – 7 = 14 + 2x

Step 3: 5x – 2x = 14 + 7

Step 4: 3x = 21

Step 5: x = 7

In which step did the student first make an error and what is the correct step? (5 points)



Step 2; 6x – 12 = 14 + 2x
Step 2; 6x – 7 = 2(6 + x + 4)
Step 3; 5x – 2x = 14 – 7
Step 3; 5x + 2x = 14 + 7
11.
Which statement is true about the equation z – z + 1 = z + 1? (5 points)


It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.
12.
What is the solution to the equation 3.6m – 2.7 = –1.8m? (5 points)


m = 0.25
m = 0.5
m = 1.25
m = 1.5

Answer 1

Question 1:

–6 + x = –3

x = -3 + 6

x = 3

Hence, the answer is C.

Question 2:

–2a + 2a + 7 = 8 

7 ≠ 8

Hence, the answer is C.

Question 3:

2(2y – 16) = 0

4y - 32 = 0

4y = 0 + 32

4y = 32

y = $\frac{32}{4}$

y = 8

Hence, the answer is C.

Question 4:

5p – 4p – 8 = –2 + 3 

p - 8 = 1

p = 1 + 8

p = 8

Hence, the answer is A.

Question 5:

4n – 2n + 4 = –1 + 17

2n + 4 = 16

2n = 16 - 4

2n = 12

n = $\frac{12}{2}$

n = 6

Hence, the answer is A.

Question 6:

2(4z – 3 – 1) = 166 – 46

8z - 6 - 2 = 120

8z = 12 + 8

8z = 20

z = $\frac{20}{8} = \frac{10}{4} = \frac{5}{2}$

z = 2.5

Hence, I think the question is wrong; it is missing a variable.

Question 7:

–x = 3 – 4x + 6

-x + 4x = 3 + 6

3x = 9

x = $\frac{9}{3}$

x = 3

Hence, the answer is C.

Question 8:

4n + 6 = 4 + 2 + 4n 

4n - 4n + 6 = 6

6 = 6

Hence, the answer is C.

Question 9:

6y + 4 = 8 + 2y + 2y

6y - 4y = 8 - 4

2y = 4

y = $\frac{4}{2}$

y = 2

Hence, the answer is B.

Question 10:

3(2x – 4) = 8 + 2x + 6

6x - 12 = 14 + 2x

6x - 2x = 14 + 12

4x = 26

x = $\frac{26}{4} = \frac{13}{2}$

x = 6.5

Hence, the answer is A.

Question 11:

z – z + 1 = z + 1

1 = z + 1

z = 1 - 1

z = 0

Hence, the answer is B.

Question 12:

3.6m – 2.7 = –1.8m

3.6m + 1.8m = 2.7

5.4m = 2.7

m = $\frac{2.7}{5.4} = \frac{1}{2}$

m = 0.5

Hence, the answer is B.

Answer 2

  Q1  Y=3 C

  Q2 7=8 C

  Q3 Y=8 C

  Q4 P=8 A

  Q5 N=6 A

  Q6 Z=2.5 C

  Q8 6=6 C

  Q9 Y=2 B

 Q10  X=6.5 A

 Q11 Z=0 B

 Q12 M=0.5 B