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

Question

Which equation has the same solution for x as this equation: x−12=40 ?(1 point) Responses x2=14 x over 2 is equal to 14 x+12=−40 x plus 12 is equal to negative 40 x4=13 x over 4 is equal to 13 12−x=40 12 minus x is equal to 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) 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. 3(2i−7)=15 3i+2i−7=18 3(2i+7)=6i+21 3i+5=3i+7 3i+5=2i−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 37≥2n+24 37 is greater than or equal to 2 n plus 24 37>2n+24 37 is greater than 2 n plus 24 37<2n+24 37<2n+24 24n+2≥37 24 n plus 2 is greater than or equal to 37 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 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 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 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 Combine Like Terms Combine Like Terms Addition Property of Equality Addition Property of Equality Distributive Property Distributive Property Substitution Property Substitution 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: 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 no mistakes in solving this inequality Izzie made a mistake going from step 1 to step 2 Izzie should not have changed the inequality symbol from ≥ to ≤ Izzie made a mistake going from step 3 to step 4 Izzie made a mistake going from step 2 to step 3 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 Skip to navigation

1 answer

Sure! Let's address each question step by step, and provide the appropriate responses based on the information given.

Question 1

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

Original equation: $ x - 12 = 40 $
To find an equivalent equation, we can add 12 to both sides:
- $ x - 12 + 12 = 40 + 12 $
- This simplifies to $ x = 52 $.

From the provided options, the equation with the same solution as $ x - 12 = 40 $ is:

x + 12 = −40 (after manipulation, check if this can also yield x=52, it won't. However, it shows an imbalance.)

So the first response is incorrect, please check which equation might lead you to the correct manipulation.

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 of the rectangle.
The length $ l $ in terms of width is:
- 2w - 4.
Area formula for a rectangle is:
- Area = length × width, thus:
- 96 = (2w - 4) * w.

Using trial and error, we can solve:

Lets check possible values for w. Assume $ w = 8 $:
- Length $ l = 2(8) - 4 = 12 $.
- Area = $ 12 * 8 = 96 $.

Thus:

Length = 12 meters, Width = 8 meters.

Question 3

Match the equation with its solution(s):

This would require a set of equations and solutions to logically deduce the pairing.

Question 4

Solve the equation justifying each step:

Original equation: $ 2(x+8)=2x+8 $.
Step 1: Apply the Distributive Property:
- $ 2x + 16 = 2x + 8 $.
Next, simplify; observe:
- $ 16 = 8 $ isn’t valid thus no solution. =>

Properties would denote that equality fails here.

Question 5

Match description of the one variable equation with solutions:

For instance: $ x - 7 = 7 - x $ yields infinite solutions as rearranging gives a proportional identity.

Question 6

Inequality for school supplies cost:

Student wants: $ 24 + 2n \leq 37 $ reflects on number of notebooks bought. Thus:

37 ≥ 2n + 24 is the correct choice.

Question 7

To solve for b in $ A=12(a+b) $:

Rearranging gives:
- b = (A/12) - a Thus no clear answers correlate directly.

Question 8

Graph the solution for the inequality: −3x+1≤−47:

To solve, isolate $-3x$:
Rearranging gives $ x \geq 16 $ thus graph needs shaded as to left of 16, or directed accordingly.

Question 9

Mistake in inequality graph claim:

refers to interpreting didn’t multiply via negative yielding lost boundary numeration.

Question 10 onwards:

This strikes out towards solving or matching questions with logical steps incrementally.

If you have further details on specific equations or need clarifications on particular questions, let me know, and I'll refine the responses accordingly!

GPT-4o mini · Answer