Which equation has the same solution for x as x−12=40
?(1 point)
Responses
12−x=40
12 minus x is equal to 40
x4=13
x over 4 is equal to 13
x2=14
x over 2 is equal to 14
x+12=−40
x+12=−40
The length of a rectangle is four meters less than twice its width.
If the area of the rectangle is 96 square meters, 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 96m^2, then the length and width are Response area
The option "\(area=\frac{1}{2}\left(l\times w\right)\)" (4 of 10) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.
An expression for the length of the rectangle in terms of the width would be \(2w-4\).
The formula for the area of a rectangle is \(A = l \times w\).
Using trial and error, if the area is 96m^2, then the length and width are 12m and 8m, respectively.
The length of a rectangle is four meters less than twice its width.
If the area of the rectangle is 96 square meters, what is the length and the width?
(3 points)
An expression for the length of the rectangle in terms of the width would be
The formula for the area of a rectangle is
Using trial and error, if the area is 96m^2, then the length and width are
WORD BANK: l= 4 -2w
l = 12 & w = 8
l = 24 & w = 4
area = 1/2 (l x w)
w - 2l - 4
l = 8 & w = 12
area = l x w
ll = 2w - 4
l = 4 & w = 24
area = 2l + 2w
An expression for the length of the rectangle in terms of the width would be \(l = 2w - 4\).
The formula for the area of a rectangle is \(A = l \times w\).
Using trial and error, if the area is 96m^2, then the length and width are \(l = 8\) and \(w = 12\).
MATCH THE EQUATION WITH ITS SOLUTION
3i + 2i - 7 = 18 ---->
3 (2i - 7) = 15 --->
3i + 5 = 2i - 7 --->
3i + 5 = 3i + 7 --->
3 (2i + 7) = 6i + 21 --->
WORD BANK: No solution, Infinite solutions, i = -12, i = 5, i = 6, i = 7, i = 11, i = 2
The matching equation and solution pairs are:
3i + 2i - 7 = 18 ---> i = 5
3 (2i - 7) = 15 ---> i = 6
3i + 5 = 2i - 7 ---> No solution
3i + 5 = 3i + 7 ---> No solution
3 (2i + 7) = 6i + 21 ---> Infinite solutions
only one word for each question
Certainly! Here are the matching equation and solution pairs with only one word for each:
3i + 2i - 7 = 18 ----> i = -12 (Solution: -12)
3 (2i - 7) = 15 ---> i = 5 (Solution: 5)
3i + 5 = 2i - 7 ---> No solution (Solution: None)
3i + 5 = 3i + 7 ---> No solution (Solution: None)
3 (2i + 7) = 6i + 21 ---> Infinite solutions (Solution: Infinite)
THE WORD BANK IS ONLY ONE EACH>
Apologies for the confusion. Here are the matching equation and solution pairs with only one word for each:
3i + 2i - 7 = 18 ----> i = 6
3 (2i - 7) = 15 ---> i = 6
3i + 5 = 2i - 7 ---> No solution
3i + 5 = 3i + 7 ---> No solution
3 (2i + 7) = 6i + 21 ---> Infinite solutions
x−7=7−x --->
3(x+5)=3x+5 --->
10−x=25 --->
2(x+4)=2x+5+3 --->
WORD BANK: One solution, No soljution, Infinite solutions
The matching equation and solution pairs are:
x−7=7−x ---> One solution
3(x+5)=3x+5 ---> No solution
10−x=25 ---> No solution
2(x+4)=2x+5+3 ---> Infinite solutions
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<2n+24
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
Solve for b in the following formula: A=12(a+b)
(1 point)
Responses
b=2A+a
b is equal to 2 cap A plus A
b=2A−a
b is equal to 2 cap A minus A
b=12A−a
b is equal to 1 half cap A minus A
b=12A+a
b=12A-a
Graph the solution set for the inequality: −3x+1≤−47
(1 point)
The solution set for the inequality −3x+1≤−47 can be graphed as a number line.
To graph the inequality, we need to isolate x on one side of the equation. First, we subtract 1 from both sides:
−3x+1−1≤−47−1
−3x≤−48
Next, we divide both sides by -3 (remembering to reverse the inequality sign when dividing by a negative number):
−3x/−3≥−48/−3
x≥16
On the number line, we can shade the region to the right of 16 to represent the solution set. Including the endpoint 16, the graph would look like this:
```
-∞ ◻=====================◼ 16 +∞
Not shaded Shaded
```
The shaded portion of the number line represents the solution set for the inequality.
can you do it in a more simple format
Apologies for the previous response. Here is a simpler representation of the solution set for the inequality −3x+1≤−47:
To graph the inequality, isolate x by subtracting 1 from both sides of the equation:
−3x+1≤−47 - 1
−3x≤−48
Next, divide both sides by -3 (remember to flip the inequality sign when dividing by a negative number):
x ≥ -48 ÷ -3
x ≥ 16
The solution set is represented by all numbers greater than or equal to 16 on the number line:
```
-∞ ---------------------●═════════════════════════► +∞
Not shaded Shaded
```
The shaded portion represents the solution set, which includes the endpoint at x = 16.
A student claims the graph below represents the solutions to the inequality −4<x
with this graph:
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 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 should have filled in the point at -4 to show the solution x could be equal to -4
The student's mistake was:
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
A student solves the following problem:
Problem:
2(x−3) + 3x = 19
Step 1: 2x − 6 + 3x = 19 Click and drag to move
Step2: (2x + 3x) −6 = 19 Click and drag to move
Step 3: 5x − 6 = 19 Click and drag to move
Step 4: 5x −6 + 6 = 19 + 6 Click and drag to move
Step 5: 5x = 25 Click and drag to move
Step 6: x = 5 Click and drag to move
What property justifies going from step 3 to step 4?
(1 point)
Responses
Addition Property of Equality
Addition Property of Equality
Substitution Property
Substitution Property
Distributive Property
Distributive Property
Combine Like Terms
Combine Like Terms
Commutative Property of Addition
The property that justifies going from Step 3 to Step 4 is the Addition Property of Equality.
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 from the previous step? Response area
What should have been the correct answer for x? Response area
The option "Combine Like Terms" (1 of 11) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.
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 from the previous step? Response area
What should have been the correct answer for x? Response area
Identify the property used to arrive at Step 1: Distributive Property
What Step includes a mistake from the previous step? Step 4
What should have been the correct answer for x? x = 5
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 (m) will it take her to only have 30 weeds remaining in the garden?(3 points)
Equation:
Solution:
Meaning of the solution in words:
Equation: 250 - 5m = 30
Solution: Solve the equation for m:
250 - 5m = 30
Subtract 250 from both sides:
-5m = 30 - 250
-5m = -220
Divide both sides by -5:
m = 44
Meaning of the solution in words: It will take Grandma 44 minutes to have only 30 weeds remaining in the garden.
The Celsius to Fahrenheit formula: F=95C+32
Solve this formula for C. Check all answers that are true.
(2 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
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.
Solution: 5/9F - 32 = C
The correct responses are:
First step is to subtract 32 from both sides.
The next step from F - 32 = 9/5 C could be to multiply both sides by 5/9.
Solution: C = (F - 32) * 5/9
zzie is trying to solve this inequality: 3(t+1)−4t≥−5
After she solves it, she shows it to you, and she asks you if she did it correctly.
This is the work she completed:
3t+3−4t≥−5
−t+3≥−5
−t≥−8
t≥8
(2 points)
True False
Izzie made no mistakes in solving this inequality
True – Izzie made no mistakes in solving this inequality
False – Izzie made no mistakes in solving this inequality
Izzie made a mistake going from step 3 to step 4
True – Izzie made a mistake going from step 3 to step 4
False – Izzie made a mistake going from step 3 to step 4
Izzie made a mistake going from step 1 to step 2
True – Izzie made a mistake going from step 1 to step 2
False – Izzie made a mistake going from step 1 to step 2
Izzie forgot to change the inequality symbol to be t≤8
True – Izzie forgot to change the inequality symbol to be t is less than or equal to 8
False – Izzie forgot to change the inequality symbol to be t is less than or equal to 8
Izzie should have had the answer t≤−8
True – Izzie should have had the answer t is less than or equal to negative 8
False – Izzie should have had the answer t is less than or equal to negative 8
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The correct response is:
True – Izzie made no mistakes in solving this inequality
true or fale EACH one
Izzie made no mistakes in solving this inequality
True – Izzie made no mistakes in solving this inequality
False – Izzie made no mistakes in solving this inequality
Izzie made a mistake going from step 3 to step 4
True – Izzie made a mistake going from step 3 to step 4
False – Izzie made a mistake going from step 3 to step 4
Izzie made a mistake going from step 1 to step 2
True – Izzie made a mistake going from step 1 to step 2
False – Izzie made a mistake going from step 1 to step 2
Izzie forgot to change the inequality symbol to be t≤8
True – Izzie forgot to change the inequality symbol to be t is less than or equal to 8
False – Izzie forgot to change the inequality symbol to be t is less than or equal to 8
Izzie should have had the answer t≤−8
True – Izzie made no mistakes in solving this inequality
False – Izzie made a mistake going from step 3 to step 4
False – Izzie made a mistake going from step 1 to step 2
False – Izzie forgot to change the inequality symbol to be t≤8
False – Izzie should have had the answer t≤−8
Solve the equation and inequality for x.
Part A: Solve the equation showing all steps.
ax−5=18
Part B: Solve the inequality showing all steps.
ax−5>18
Answer these Questions:
1. Describe the number line set up that would show all of the solutions for the inequality in Part B.
2. State the difference between solving an equation and an inequality.
(4 points)
Part A: Solving the equation ax−5=18
To solve the equation, we'll isolate x by performing the necessary operations:
ax - 5 = 18
First, we'll add
olve the equation and inequality for x.
Part A: Solve the equation showing all steps.
ax−5=18
Part B: Solve the inequality showing all steps.
ax−5>18
Answer these Questions:
1. Describe the number line set up that would show all of the solutions for the inequality in Part B.
2. State the difference between solving an equation and an inequality.
(4 points)