An expression for the length of the rectangle in terms of the width would be Response area

Question

The formula for the area of a rectangle is Response area

Using trial and error, if the area is 96 m^2, then the length and width are Response area

Question 4
3. Match the equation with its solution(s).(5 points)
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3i+5=3i+7
3i+2i−7=18
3i+5=2i−7
3(2i+7)=6i+21
3(2i−7)=15
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 Response area simplified equation

Step 2: Response area 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

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

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

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

37<2n+24
37<2n+24
Question 8
7. Solve for b in the following equation: A=12(a+b)
(1 point)
Responses

b=2A−a
b is equal to 2 cap A minus A

b=2A+a
b is equal to 2 cap A plus A

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

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

Addition Property of Equality
Addition Property of Equality

Commutative Property of Addition
Commutative Property of Addition

Combine Like Terms
Combine Like Terms

Substitution Property
Substitution Property

Distributive Property
Distributive Property
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? Response area

What should have been the correct answer for x ? Response area

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:
250 - 5m = 30

Solution:
m = 44

Meaning of the solution in words:
It will take her 44 minutes to have 30 weeds remaining.

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 2 to step 3

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

Izzie made a mistake going from step 1 to step 2

Izzie made a mistake going from step 3 to step 4

Izzie made no mistakes in solving this inequality

The correct answer should have been t≤8

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

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page 5 of 5

Answer 1

Here's how you can respond to each question based on the information given:

Question 1

• Expression for Length in terms of Width (w):
  \[ \text{Length} = \frac{\text{Area}}{\text{Width}} = \frac{96}{w} \]

• Formula for Area of Rectangle:
  \[ \text{Area} = \text{Length} \times \text{Width} \]

• Using trial and error for Area = 96 m²:
  Let's say width (w) = 8 m, then length = \( \frac{96}{8} = 12 \) m.
  Width (w) = 12 m gives length = \( \frac{96}{12} = 8 \) m.

Question 4

Match the equations with their solutions:

• 3i + 5 = 3i + 7: No solutions
• 3i + 2i − 7 = 18: \( i = 4 \)
• 3i + 5 = 2i − 7: \( i = -12 \)
• 3(2i + 7) = 6i + 21: True for all i
• 3(2i − 7) = 15: \( i = 10 \)

Question 5

Step 1 property: Distributive Property
Simplified equation: \( 2x + 16 = 2x + 8 \)

Step 2 property: Subtraction Property of Equality
Simplified equation: \( 16 = 8 \)

Question 6

Match the equations with their number of solutions:

• x − 7 = 7 − x: Infinite solutions (All x)
• 3(x + 5) = 3x + 5: One solution
• 10 − x = 25: One solution
• 2(x + 4) = 2x + 5 + 3: No solution

Question 7

The inequality that describes the scenario is:
37 ≥ 2n + 24
This means the student can't spend more than $37 on notebooks.

Question 8

To solve for b in \( A = 12(a + b) \):
b = (A/12) - a (this wasn't one of the responses provided - the correct simplification is b = A/12 - a).

Question 9

To graph the inequality \( -3x + 1 ≤ -47 \):

1. Solve for \( x \):
   \( -3x ≤ -48 \)
   \( x ≥ 16 \) (area on the right of 16).

Question 10

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

Question 11

Property from Step 3 to Step 4: Addition Property of Equality

Question 12

• Property used at Step 1: Distributive Property
• Mistake made from Step 2: Step 4 should simplify \( 3x + 2 \) to \( 3x = 17 - 2 \) instead.
• Correct answer for x: \( x = 5 \)

Question 13

• Meaning of the solution: It will take her 44 minutes to reach 30 weeds remaining.

Question 14

True steps regarding solving the formula for C:

• First step is to add 32 to both sides.
• The next step could also be to multiply both sides by 5.
• The solution: \( C = \frac{5}{9}(F - 32) \)

Question 15

• Responses about Izzie's work:
  True:
• Izzie made no mistakes in solving this inequality. False:
• Izzie made a mistake going from step 2 to step 3.
• Izzie should not have changed the inequality symbol from ≥ to ≤.
• Izzie made a mistake going from step 1 to step 2.
• Izzie made a mistake going from step 3 to step 4.
• The correct answer should have been t ≤ 8.

Question 16

To graph the inequality \( 5n - 3 < 3(n + 1) \):

1. Simplify: \( 5n - 3 < 3n + 3 \)
2. This leads to: \( 2n < 6 \)
3. Thus: \( n < 3 \) (to the left of 3 on a number line).

Please insert these answers in your format as required.