. Which equation has the same solution for x as this equation: x−12=40

Question

?(1 point)
Responses

x4=13
x over 4 is equal to 13

12−x=40
12 minus x is equal to 40

x2=14
x over 2 is equal to 14

x+12=−40
x plus 12 is equal to negative 40
Question 3
2. The length of a rectangle is four meters less than twice its width.

If the area of the rectangle is 96 m^2, what is the length and the width?

(3 points)
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An expression for the length of the rectangle in terms of the width would be Response area

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=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: Response area Property to get Response area simplified equation

Step 2: Response area Property to get Response area simplified equation

For this equation, there is/are Response area

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: Response area

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:

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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Answer 1

Sure, let’s go through each question you have along with potential solutions.

Question 1

Given equation: \(x − 12 = 40\)

We can rewrite this equation to find the equivalent: \[x = 40 + 12\] \[x = 52\]

Now, we check the given options for equivalent equations:

• Option 1: \( x/4 = 13\) (not equivalent, gives \(x = 52\), but not the same form)
• Option 2: \(12 − x = 40\) (not equivalent, gives different result)
• Option 3: \( x/2 = 14\) (not equivalent)
• Option 4: \(x + 12 = -40\) (not equivalent)

Thus, there may be a mistake with the choices listed, as none of them yield the same solution as the initial equation. Ensure to recheck the options provided.

Question 2

1. The length of the rectangle \( L \) in terms of width \( W \):

   • Length \( L = 2W - 4 \) (since "four meters less than twice its width")

2. Area formula:

   • Area \( A = L \times W \)

3. Substitute:

   • \( 96 = (2W - 4)W \)
   • Solve this to find \( W \) and then find \( L \).

Question 3

Match the equations with their solutions. Without the equations listed, it's hard to match, but you would typically look for simplifications and the resulting equalities.

Question 4

Justify each step for equation \( 2(x+8) = 2x + 8 \):

1. Step 1: Distributive Property. \[2(x+8) = 2x + 16\]
2. Step 2: Subtraction Property of Equality to get to \( 16 = 8 \).

Result will show inconsistency hence there are zero solutions.

Question 5

For each description, you need to identify whether the solution is:

• Infinite solutions
• No solution
• One solution

Question 6

In this case, you'd want to find which inequality accurately reflects the financial situation. The student will find: \[37 - 24 > 2n\] leads to the response: \[37 > 2n + 24\]

Question 7

Would solve the equation: \[ A = 12(a+b) \] to isolate \( b \).

Question 8

The graph for the inequality will be found by isolating \( x \):

• Solve for \( x \): \[ -3x ≤ -48 \] gives \( x ≥ 16 \).

Question 9

The inequalities must be expressed and justified correctly.

Question 10

If working through solving \( 2(x-3)+3x=19 \):

• Proper justification would be Distributive Property.

Question 11

For the equation \( x+2(x+1)=17 \):

1. Combine Like Terms (Step 1).
2. Incorrectly concluded values would need re-evaluation. The correct value for \( x \) would be \( x = 5 \).

Question 12

For Grandma's scenario,

• Setting up the equation: \[ 250 - 5t = 30 \]

Meaning of the solution would refer to total time required.

Question 13

To solve \( F = \frac{9}{5}C + 32\) for \( C \):

• Manipulation via properties would be outlined.

Question 14

For \( 3(t+1) - 4t ≥ -5 \): The steps are potentially error-prone, the evaluation needs confirmation for correctness.

Question 15

For \( 5n - 3 < 3(n + 1) \), analyzing inequality direction and operations give insight into generated solutions.

Final Guidance:

Each question leads to a layered approach requiring attention to detail. Please review any numerical results in your math work entirely to ensure optimal outcomes.