Match the equation with its solution(s).(5 points)

Question

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3i+5=2i−7
3i+5=3i+7
3(2i+7)=6i+21
3(2i−7)=15
3i+2i−7=18

Answer 1

3i+5=2i−7 -> -12
3i+5=3i+7 -> no solution
3(2i+7)=6i+21 -> no solution
3(2i−7)=15 -> i=8
3i+2i−7=18 -> i=5

Answer 2

show me a step by step on how you got those answers

Answer 3

Sure! Here is a step-by-step explanation for each equation:

1) 3i+5=2i-7:
To solve this equation, we want to isolate the variable "i" on one side.
Subtract 2i from both sides:
3i - 2i + 5 = 2i - 2i - 7 -> i + 5 = -7
Subtract 5 from both sides:
i + 5 - 5 = -7 - 5 -> i = -12

2) 3i+5=3i+7:
To solve this equation, again we want to isolate the variable "i".
Subtract 3i from both sides:
3i - 3i + 5 = 3i - 3i + 7 -> 5 = 7
Since 5 is not equal to 7, there is no solution for this equation.

3) 3(2i+7)=6i+21:
Start by distributing 3 to the terms inside the parentheses:
6i + 21 = 6i + 21
Both sides are already equal, so this equation is true for all values of "i". There are infinitely many solutions for this equation.

4) 3(2i-7)=15:
Distribute 3 to the terms inside the parentheses:
6i - 21 = 15
Add 21 to both sides:
6i - 21 + 21 = 15 + 21 -> 6i = 36
Divide both sides by 6:
(6i)/6 = 36/6 -> i = 6
So the solution to this equation is i = 6.

5) 3i+2i-7=18:
Combine like terms on the left side of the equation:
5i - 7 = 18
Add 7 to both sides:
5i - 7 + 7 = 18 + 7 -> 5i = 25
Divide both sides by 5:
(5i)/5 = 25/5 -> i = 5
Therefore, the solution to this equation is i = 5.

I hope this helps clarify the steps taken to solve each equation!

Answer 4

Solve the equation justifying with the correct reasoning: 2(x+8)=2x +8
(5 points)
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2(x+8)=2x +8
Step 1: Response area Property to get Response area

Step 2: Response area Property to get Response area

For this equation, there is/are Response area

Answer 5

For this equation, there is one solution.

Step 1: Distribute the 2 on the left side of the equation:

2(x+8) = 2x + 8
2x + 16 = 2x + 8

Step 2: Simplify the equation by subtracting 2x from both sides:

2x - 2x + 16 = 2x - 2x + 8
16 = 8

Since 16 is not equal to 8, this equation has no solution.

Answer 6

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

Answer 7

x−7=7−x -> one solution
3(x+5)=3x+5 -> infinitely many solutions
10−x=25 -> no solution
2(x+4)=2x+5+3 -> no solution

Answer 8

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<2n+24

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

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

Answer 9

37 ≥ 2n + 24

Answer 10

Solve for b in the following formula: A=1/2(a+b)
(1 point)
Responses

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

b=2A−a
b is equal to 2 cap A minus A

b=2A+a

Answer 11

b=2A-a

Answer 12

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

Answer 13

To graph the solution set for the inequality −3x + 1 ≤ −47, we will first solve the inequality for x:

−3x + 1 ≤ −47
Subtract 1 from both sides:
−3x ≤ −48
Divide both sides by −3 (remember that when dividing by a negative number, the direction of the inequality symbol changes):
x ≥ 16

Now, we can graph the solution set on the number line. Since the inequality is "x is greater than or equal to 16," we will have a closed dot at 16 and shade to the right:

---------------------●----------------->

The shaded area to the right of the dot represents the solution set for the inequality.

Answer 14

graph −4<x

Answer 15

To graph the solution set for the inequality -4 < x, we will represent it on a number line:

---------------●------------------->

Since the inequality is "x is greater than -4," we have an open circle at -4 and shade to the right. The shaded area to the right of -4 represents the solution set for the inequality.

Answer 16

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

Substitution Property
Substitution Property

Commutative Property of Addition
Commutative Property of Addition

Addition Property of Equality
Addition Property of Equality

Distributive Property
Distributive Property

Combine Like Terms

Answer 17

The property that justifies going from step 3 to step 4 is the Addition Property of Equality.

Answer 18

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

Answer 19

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: Length x Width.

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

Length = 12 meters
Width = 8 meters

Answer 20

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

Answer 21

Identify the property used to arrive at Step 1: The property used to arrive at Step 1 is the Distributive Property.

What Step includes a mistake from the previous step? Step 4 includes a mistake from the previous step.

What should have been the correct answer for x? The correct answer for x should have been x = 5.

Answer 22

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:

Answer 23

Equation: 250 - 5m = 30

Solution:
To solve the equation, we will isolate the variable "m".

Subtract 250 from both sides:
250 - 5m - 250 = 30 - 250
-5m = -220

Divide both sides by -5:
(-5m) / -5 = -220 / -5
m = 44

Meaning of the solution in words:
It will take Grandma 44 minutes to remove enough weeds so that only 30 weeds remain in the garden.

Answer 24

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.

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

Solution: 5/9F - 32 = C
Solution: 5/9F - 32 = C

First step is to add 32 to both sides.
First step is to add 32 to both sides.

To solve this equation for C, you would have to distribute at some point.

Answer 25

To solve the formula F=95C+32 for C, we can follow these steps:

First step is to subtract 32 from both sides:
F - 32 = 95C

Next step is to divide both sides by 95:
(F - 32)/95 = C

Solution: (F - 32)/95 = C

To check if the solution is true, we can substitute the value of C back into the original equation F=95C+32 and see if it holds.

Answer 26

The Celsius to Fahrenheit formula: F=9/5C+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.

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

Solution: 5/9F - 32 = C
Solution: 5/9F - 32 = C

First step is to add 32 to both sides.
First step is to add 32 to both sides.

To solve this equation for C, you would have to distribute at some point.

Answer 27

To solve the formula F=9/5C+32 for C, we can follow these steps:

First step is to subtract 32 from both sides:
F - 32 = 9/5C

Next step is to multiply both sides by 5/9:
(5/9)(F - 32) = C

Solution: (5/9)(F - 32) = C

To check if the solution is true, we can substitute the value of C back into the original equation F=9/5C+32 and see if it holds.

Answer 28

only use these answers:
First step is to multiply by 9 on each side.
First step is to multiply by 9 on each side.

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

Solution: 5/9F - 32 = C
Solution: 5/9F - 32 = C

First step is to add 32 to both sides.
First step is to add 32 to both sides.

To solve this equation for C, you would have to distribute at some point.

Answer 29

To solve the formula F=9/5C+32 for C, we can follow these steps:

First step is to subtract 32 from both sides:
F - 32 = 9/5C

Next step is to multiply both sides by 5/9:
(5/9)(F - 32) = C

Solution: (5/9)(F - 32) = C

Answer 30

Izzie 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

Answer 31

Izzie made no mistakes in solving this inequality.
True – Izzie made no mistakes in solving this inequality

Answer 32

True False answer all quiestions
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

Answer 33

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.
- False – Izzie made a mistake going from step 3 to step 4

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.
-