Match the equation with its solution(s).(5 points)

Question

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3i+5=2i−7
3(2i−7)=15
3i+5=3i+7
3i+2i−7=18
3(2i+7)=6i+21
Question 5
4. Solve the equation justifying each step with the correct reasoning.

2(x+8)=2x+8
(5 points)
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Step 1: Property to get simplified equation

Step 2: Property to get simplified equation

For this equation, there is/are

Properties and Reasons
Equation simplified
Question 6
5. Match the description of the one variable equation with the number of solutions it will have.(4 points)
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x−7=7−x
3(x+5)=3x+5
10−x=25
2(x+4)=2x+5+3
Question 7
6. A student wants to purchase some new school supplies. He wants to buy a calculator that costs $24 and some notebooks for school. Each notebook costs $2. The student only has $37 to spend.

Let n represent the number of notebooks that he buys.

Which inequality describes this scenario?

(1 point)
Responses

37>2n+24
37 is greater than 2 n plus 24

24n+2≥37
24 n plus 2 is greater than or equal to 37

37<2n+24
37<2n+24

37≥2n+24
37 is greater than or equal to 2 n plus 24
Question 8
7. Solve for b in the following equation: A=12(a+b)
(1 point)
Responses

b=12A−a
b is equal to 1 half cap A minus A

b=2A−a
b is equal to 2 cap A minus A

b=12A+a
b is equal to 1 half cap A plus A

b=2A+a
b is equal to 2 cap A plus A
Question 9
8. Graph the solutions for the inequality: −3x+1≤−47
(2 points)
Responses

Question 10
9. A student claims that graph below represents the solutions to the inequality: −4<x

What was the student's mistake?

(1 point)
Responses

The student should have multiplied by a negative and switched the direction of the arrow on the graph to go right instead of left
The student should have multiplied by a negative and switched the direction of the arrow on the graph to go right instead of left

The student did not make a mistake; this is the correct graph of the inequality
The student did not make a mistake; this is the correct graph of the inequality

The student did x is less than -4, when the variable is on the other side; -4 is less than x so x is greater than -4
The student did x is less than -4, when the variable is on the other side; -4 is less than x so x is greater than -4

The student should have filled in the point at -4 to show the solution x could be equal to -4
The student should have filled in the point at -4 to show the solution x could be equal to -4
Question 11
10. A student solves the following equation:

Problem: 2(x−3)+3x=19
Step 1: 2x−6+3x=19
Step 2: (2x+3x)−6=19
Step 3: 5x−6=19
Step 4: 5x−6+6=19+6
Step 5: 5x=25
Step 6: x=5
What property justifies going from step 3 to step 4?

(1 point)
Responses

Substitution Property
Substitution Property

Distributive Property
Distributive Property

Commutative Property of Addition
Commutative Property of Addition

Addition Property of Equality
Addition Property of Equality

Combine Like Terms
Combine Like Terms
Question 12
11. A student solved the equation: x+2(x+1)=17
Step 1: x+2x+2=17
Step 2: 3x+2=17
Step 3: 3x=15
Step 4: x=45
(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Identify the property used to arrive at Step 1:

What step includes a mistake made from the previous step?

What should have been the correct answer for x ?

Question 13
12. Grandma is removing weeds from her garden. She estimates that there are 250 weeds in the garden at the moment, and she can remove weeds at a rate of 5 per minute. At this rate, how many minutes will it take her to only have 30 weeds remaining in the garden?(3 points)
Equation:

Solution:

Meaning of the solution in words:

Question 14
13. The Celsius to Fahrenheit formula: F=95C+32
Solve this formula for C. Check all answers that are true.

(4 points)
Responses

First step is to multiply by 9 on each side.
First step is to multiply by 9 on each side.

First step is to add 32 to both sides.
First step is to add 32 to both sides.

The next step from F - 32 = 9/5 C, could be to multiply both sides by 5
The next step from F - 32 = 9/5 C, could be to multiply both sides by 5

The next step from F - 32 = 9/5 C, could be to divide both sides by 5
The next step from F - 32 = 9/5 C, could be to divide both sides by 5

Solution: 5/9F - 32 = C
Solution: 5/9F - 32 = C

To solve this equation for C, you would have to distribute at some point.
To solve this equation for C, you would have to distribute at some point.
Question 15
14. Izzie is trying to solve this inequality: 3(t+1)−4t≥−5
After she solves it, she shows it to you and asks you if she did it correctly.

This is the work she completed:

Step 1: 3t+3−4t≥−5
Step 2: −t+3≥−5
Step 3: −t≥−2
Step 4: t≤2


(12 points)
True False
Izzie made a mistake going from step 1 to step 2

Izzie made no mistakes in solving this inequality

The correct answer should have been t≤8

Izzie made a mistake going from step 3 to step 4

Izzie made a mistake going from step 2 to step 3

Izzie should not have changed the inequality symbol from ≥
to ≤

Question 16
15. Which graph represents the solutions to this inequality: 5n−3<3(n+1)
(2 points)
Responses

Question 17
Solve the following for a: ax−5>18
(1 point)
Responses

a = 23x
a = 23x

a = 23+x
a = 23+x

a > 23x
a > 23x

a > 13x
a > 13x
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page 5 of 5

Answer 1

Let's go through each question step-by-step to provide the necessary responses.

Question 5

Match the equation with its solution(s).
For 3i + 5 = 2i - 7 the solution is 3i - 2i = -7 - 5, which leads to i = -12.

1. 3i + 5 = 2i - 7 matches with 3i + 2i - 7 = 18, moving terms to one side.

Question 6

Match the description of the one variable equation with the number of solutions it will have.

1. x - 7 = 7 - x is infinitely many solutions since it simplifies to 0 = 0.
2. 3(x + 5) = 3x + 5 has one solution (it simplifies to a false statement).
3. 10 - x = 25 has one solution (x = -15).
4. 2(x + 4) = 2x + 5 + 3 has no solutions (it simplifies to a contradiction).

Question 7

Which inequality describes this scenario?
The student can spend a total of $37, which must be greater than the cost of the calculator and the notebooks. Therefore, the correct inequality is: 37 ≥ 2n + 24

Question 8

Solve for b in the following equation: A = 12(a + b)
To isolate b, we first rearrange:

1. A = 12a + 12b
   Thus, b = (A - 12a)/12

So, the correct response is b = 12A - a (though the expression seems off; check original context).

Question 9

Graph the solutions for the inequality: -3x + 1 ≤ -47
To solve for x: -3x ≤ -48
x ≥ 16

This implies a graph on the number line where x is greater than or equal to 16.

Question 10

What was the student's mistake regarding the graph for -4 < x?
The correct response would be:
The student should have multiplied by a negative and switched the direction of the arrow on the graph to go right instead of left.

Question 11

What property justifies going from step 3 to step 4?
The correct response is: Addition Property of Equality (adding 6 to both sides).

Question 12

1. Identify the property used to arrive at Step 1:
   Distributive Property
2. What step includes a mistake made from the previous step?
   Step 4: (should have been x = 5).
3. What should have been the correct answer for x?
   x = 5.

Question 13

Grandma's estimates:

1. Equation: 250 - 5t = 30
2. Solution: t = 44 minutes (250 - 30 = 5t ➔ 220 = 5t ➔ t = 220/5).
3. Meaning of the solution in words: It will take Grandma approximately 44 minutes to remove the weeds to have only 30 remaining.

Question 14

Celsius to Fahrenheit formula: F = 9/5C + 32
Check all true statements:

• First step is to add 32 to both sides. (true)
• The next step could be to multiply both sides by 5. (true)
• The next step could be to divide both sides by 5. (true)
• First step is to multiply by 9 on each side. (false)

Solution: C = 5/9(F - 32)

Question 15

Evaluate Izzie's work on solving the inequality:

• Izzie made a mistake going from step 2 to step 3: True
• Izzie made no mistakes in solving this inequality: False
• The correct answer should have been t ≤ 8: False
• Izzie made a mistake going from step 3 to step 4: False
• Izzie made a mistake going from step 2 to step 3: True
• Izzie should not have changed the inequality symbol from ≥ to ≤: False

Question 16

Which graph represents the solutions to: 5n - 3 < 3(n + 1)?
This requires solving and graphing.

Question 17

Solve for a in ax - 5 > 18:

1. ax > 23
2. a > 23/x.

So the correct response is: a > 23x.

You can now take the responses above as needed. Let me know if you require any further assistance!