Which equation has the same solution for x as this equation: x−12=40 ?(1 point) Responses x+12=−40 x plus 12 is equal to negative 40 x2=14 x over 2 is equal to 14 12−x=40 12 minus x is equal to 40 x4=13 x over 4 is equal to 13 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) 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. 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) 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. 3i+5=2i−7 3(2i+7)=6i+21 3i+2i−7=18 3(2i−7)=15 3i+5=3i+7 Question 5 4. Solve the equation justifying each step with the correct reasoning. 2(x+8)=2x+8 (5 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. 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) 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. 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 372n+24 37 is greater than 2 n plus 24 37≥2n+24 37 is greater than or equal to 2 n plus 24 37

Question

Which equation has the same solution for x as this equation: x−12=40 ?(1 point) Responses x+12=−40 x plus 12 is equal to negative 40 x2=14 x over 2 is equal to 14 12−x=40 12 minus x is equal to 40 x4=13 x over 4 is equal to 13 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) 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. 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) 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. 3i+5=2i−7 3(2i+7)=6i+21 3i+2i−7=18 3(2i−7)=15 3i+5=3i+7 Question 5 4. Solve the equation justifying each step with the correct reasoning. 2(x+8)=2x+8 (5 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. 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) 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. 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 plus A b=12A−a b is equal to 1 half 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 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 Commutative Property of Addition Commutative Property of Addition Substitution Property Substitution Property Combine Like Terms Combine Like Terms Distributive Property Distributive Property Addition Property of Equality Addition Property of Equality 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: 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 no mistakes in solving this inequality Izzie should not have changed the inequality symbol from ≥ to ≤ Izzie made a mistake going from step 2 to step 3 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 1 to step 2 Question 16 15. Which graph represents the solutions to this inequality: 5n−3<3(n+1) (2 points) Responses Skip to navigation

1 answer

Let's address each question step by step.

Question 1

Which equation has the same solution for x as this equation: x−12=40? To solve the original equation:

$ x - 12 = 40 $
Add 12 to both sides: $ x = 40 + 12 = 52 $

Now we find an equation that also has $ x = 52 $.

Checking the options:
- $ x + 12 = -40 $ → No
- $ x^2 = 14 $ → No
- $ 12 - x = 40 $ → Rearranging gives $ x = -28 $ → No
- $ x/4 = 13 $ → This gives $ x = 52 $

Correct Answer: $ x/4 = 13 $

Question 2

The length of a rectangle is four meters less than twice its width. If the area of the rectangle is 96 m², what is the length and the width?

Let $ w $ be the width. Then, the length $ l = 2w - 4 $.
The area is given by $ area = l \times w = 96 $. Thus, we have: \[ (2w - 4)w = 96 \] Expanding and rearranging gives: \[ 2w^2 - 4w - 96 = 0 \] Divide through by 2: \[ w^2 - 2w - 48 = 0 \] Factor: \[ (w - 8)(w + 6) = 0 \] So, $ w = 8 $ (width must be positive, discard $-6$).

Finding the length: \[ l = 2(8) - 4 = 16 - 4 = 12 \]

Thus, width = 8 m and length = 12 m.

Question 3

Match equations with their solutions. We can help you match given equations, but you'll need to provide the full list of equations and solutions.

Question 4

Solve: 2(x+8)=2x+8.

Expand left side: $ 2x + 16 = 2x + 8 $
Subtract $ 2x $ from both sides: $ 16 = 8 $

Thus, this results in a contradiction.

Conclusion: There are no solutions (the equation is inconsistent).

Question 5

Match equation with the number of solutions. Again, please provide the specific equations and descriptors so I can help with matching.

Question 6

Describe the inequality for the student buying supplies. Let $ n $ be the number of notebooks: \[ 24 + 2n \leq 37 \]

This translates to: \[ 37 \geq 2n + 24 \]

Correct response: $ 37 \geq 2n + 24 $

Question 7

Solve for b in the equation $ A = 12(a+b) $.

Start with the equation: \[ A = 12a + 12b \]
Rearranging gives: \[ 12b = A - 12a \]
Therefore: \[ b = \frac{A - 12a}{12} \]

None of the provided answers match this form. Can you double-check?

Question 8

Graphing the inequality $ -3x + 1 \le -47 $.

Rearranging gives: \[ -3x \le -48 \quad \Rightarrow \quad x \ge 16 \]

You would graph it and shade to the right of $ x = 16 $ with a closed dot.

Question 9

What was the student's mistake with the graph of $ -4 < x $? The error is: "The student confused the inequality direction - it should show $ x > -4 $."

Question 10

Identify property from steps of solving: From $ Step 3: 5x - 6 = 19 $ to $ Step 4: 5x = 25 $:

The justification is Addition Property of Equality.

Question 11

Identify property and mistakes in solving $ x + 2(x + 1) = 17 $.

Step 1 Property: Distributive Property
Mistake in Step: Error occurs in the last step when dividing: should be $ x = 5 $, not 45.
Correct answer for x: $ x = 5 $.

Question 12

Weeds in the garden scenario. Total initial weeds = 250. Weeds to remain = 30. Weeds to be removed = 250 - 30 = 220. At a rate of 5 per minute: \[ 220 / 5 = \text{44 minutes} \] So, it will take her 44 minutes to have 30 weeds remaining.

Question 13

Celsius to Fahrenheit formula: Starting from: \[ F = \frac{9}{5}C + 32 \]

Rearranging for C involves:

Subtracting 32 from both sides: \[ F - 32 = \frac{9}{5}C \]
Last step: multiply by $ \frac{5}{9} $ Thus:

True statements to check:

The first step is to subtract 32 from both sides. True.
Correct answer should involve multiplying for the final rearrangement.

Question 14

Analyzing Izzie's inequality steps:

True: Izzie made no mistakes in solving the inequality.
False: She did change the inequality symbol correctly.
False: The correct answer was not stated.

If you need further clarifications or different sections completed, please say so!

GPT-4o mini · Answer