Kelsey solved the following equation:

7x − one over two (8x + 2) = 6

Step Work Justification
1 7x − 4x − 1 = 6
2 3x − 1 = 6
3 3x = 7
4 x = 7 over 3
Which of the following has all of the correct justifications Kelsey used to solve this equation?

Question 8 options:

1. Distributive property 2. Combine like terms 3. Addition property of equality 4. Division property of equality


1. Multiplication property of equality 2. Combine like terms 3. Addition property of equality 4. Division property of equality


1. Distributive property 2. Combine like terms 3. Subtraction property of equality 4. Division property of equality


1. Multiplication property of equality 2. Combine like terms 3. Subtraction property of equality 4. Division property of equality

Answers

Answer 1

9514 1404 393

Answer:

  (a) 1. Distributive property 2. Combine like terms 3. Addition property of equality 4. Division property of equality

Step-by-step explanation:

Replacement of -1/2(8x +2) by -4x -1 is use of the distributive property, eliminating choices B and D.

In step 3, addition of 1 to both sides of the equation is use of the addition property of equality, eliminating choice C. This leaves only choice A.

_____

Additional comment

This problem makes a distinction between the addition property of equality and the subtraction property of equality. They are essentially the same property, since addition of +1 is the same as subtraction of -1. The result shown in Step 3 could be from addition of +1 to both sides of the equation, or it could be from subtraction of -1 from both sides of the equation.

In general, you want to add the opposite of the number you don't want. Here, that number is -1, so we add +1. Of course, adding an opposite is the same as subtracting.

In short, you can argue both choices A and C have correct justifications. The only reason to prefer choice A is that we usually think of adding positive numbers as addition, and adding negative numbers as subtraction.

Answer 2

Answer:1. Distributive property 2. Combine like terms 3. Addition property of equality 4. Division property of equality

Step-by-step explanation:


Related Questions

Find the area of each shaded region. Show your reasoning.

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maybe we could answer if there waas a pic=]

Factor x^2+x+6
Plz help

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Answer:

2

Step-by-step explanation:

PLEASE HELP WITH THE SCREENSHOT BELOW

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Answer:

32.8

Step-by-step explanation:

well you need to use soh cah toa. so here we would use sin since we get an opposite side and a hypotenuse. so 45/83 would give us the sin of the sides but since we need to find the angle we take the sin inverse which gives us 32.83139231 which rounds to 32.8

PLEASEEE HELP!!!!!!!

Temperatures in Verkhoyansk, Russia have been recorded as low as -90°F and
as high as 98°F. What is the difference between the highest and lowest recorded
temperatures in Verkhoyansk?

Answers

Hi,

The difference is 188 F

If y= 2x+3, find the value of y when x= 2.

Answers

Answer:

7

Step-by-step explanation:

subtitue x=2 in given equation as:

y= 2(2)+3

y= 4+3

y=7

Can someone pls help me pls ​

Answers

Answer:

your fractions will go in order of 1/4, 2/5, 5/8, 4/6

Step-by-step explanation:

a. 2/5 < 1/2 and 4/6 > 1/2 so 2/5 < 4/6

b. 5/8 > 1/2 and 1/4 < 1/2 so 5/8 > 1/4

c. 4/6 > 1/2 and 4/6 < 2/2 and 5/8 > 1/2 and 5/8 < 2/2 and 5/8  ?? cannot see this

Which of the following fractions converts to a repeating decimals

Answers

Step-by-step explanation:

The answer is a option.

hope it helps

option A I believe :)

mathematics geniuses where are you ? help me answer this question please.

Answers

Step-by-step explanation:

There is 7 blocks that measure is 12.0-12.2

11 blocks that measure 12.2 to 12.4

18 blocks that measure 12.4 to 12.6

10 blocks that measure 12.6-12.8

4 blocks that measure 12.8 to 13.0

We can't find a mean by with Intervals so let find the midpoint of each interval,

12.1, 12.3, 12.5, 12.7, 12.9.

12.1 occurs 7 times so that equal 12.1 x 7=84.712.3 occurs 11 times so that equal 12.3 x 11=135.312.5 occurs 18 times so that equal 12.5x18=22512.7 occurs 10 times so that equal 12.7x10=12712.9 occurs 4 times 12.9×4=51.6

Add up the products and divide them by 50

[tex]\frac{623.6}{50} = 12.472[/tex]

Standard Deviation is

0.23( it is alot of steps so I use a calculator to save time).

The interqualtie range is 0.4

Add or Subtract: show all written work 30 POINTS!!

Answers

Answer:

I hope it helped U

stay safe stay happy

Solve 2/5 x + 1/2 = 5/6

Answers

The answer is x= 5/6

Answer:

5/6

Step-by-step explanation:

I'm assuming the x in your equation is used as a variable.

5/6-1/2= 2/6=1/3

2/5x=1/3

x=5/6

What is the coefficient of the x-term in the expression 4x+5xy-2y

Answers

Answer: here the answer is 4

PLS HELPPPPPPPPPppppppp

Answers

collinear mean the point are lie on the same line.
H,A and S
H,D and S
Y, D and T
All correct

P, H and A not lie on the same line (not collinear)

Barry is checking his bank account for a few transactions that he completed. He had $230
in his account to start and then contributed a check for $360. He paid his water, electric and
cable bill, which were $100, $46 and $107. How much money is in his bank account?

A. $253
B. $383
C. $590
D. $337

Answers

Answer:

D.

Step-by-step explanation:

$230 + $360 = $590

$590 - $253* = $337

$337

*( total sum of all the bills )

Complete the equation. (x-2)(x^2 + 2x + 4) = ( , )

Answers

Answer:

Step-by-step explanation:

x(x² + 2x + 4)-2((x² + 2x + 4)

x³+2x²+4x -2x²-4x-8

x³-8

I need help ASAP whit this question

Answers

Answer:

B. 7

Step-by-step explanation:

The original box must be 1 by 1 by 1.

So then the new box would be 2 by 2 by 2.

2×2×2=8

8-1=7

I hope this helps!

pls ❤ and mark brainliest pls!

If there are 2.54 centimeters in 1 inch, how long in inches is a meter stick? Hint: There are 100 centimeters in 1 meter. Round your answer to the nearest hundredth.

Answers

Answer:

i dont know that well but i do know 1 meter is roughly 2ft, so id say about 25.5 inches

0.01 inch is the  length of a meter stick.

To find the length of a meter stick in inches, we can use the conversion factor:

1 meter = 100 centimeters

1 inch = 2.54 centimeters

We can set up the proportion:

1 meter / 100 centimeters = x inches / 1 inch

Cross-multiplying:

1 meter × 1 inch = 100 centimeters × x inches

x = (1 meter × 1 inch) / (100 centimeters)

x = 1 inch / 100

x = 0.01 inch

To learn more on Conversion factor click:

https://brainly.com/question/32020768

#SPJ6

4v + 1) + v = 5(v - 1) +9

Answers

Answer:

Step-by-step explanation:

4(v+1)+v=5(v-1)+9

distribute

4v+4+v

which is

5v+4=5v-5+9

5v+4=5v+4

No solution is the answer

The following dotplot shows the centuries during which the 11 castles whose ruins remain in Somerset, England were constructed. Each dot represents a different castle.

According to the 1.5.IQR rule for outliers, how many high outliers are there in the data set?

Choose 1 answer:

Answers

Taking into account the rule 1.5 IQR, there aren't high outliers in the displayed data set.

Calculation of the Interquartile Range and the rule 1.5 IQR.

To calculate the Interquartile Range IQR, you must subtract the value of the first quartile Q1, to the third quartile Q3, as you can see in the formula below:

IQR = Q3 - Q1

Using the five-number summary, you can replace the formula:

IQR = 17 - 13IQR = 4

Before to apply the rule 1.5 IQR, you must multiply the IQR by 1.5:

4 * 1.5 = 6

Now, to apply the rule you must add the value obtained (6), to the third quartile (17), if any data is over this, theoretically it's an outlier:

17 + 6 = 23 (As you do not have any data over this value, it is identified that there are no outliers in the upper section).

Finally, you must subtract the value obtained (6) to the first quartile (13), if any data is under this, theoretically it's an outlier:

13 - 6 = 7 (Since you don't have any castle data built before this century, there wouldn't be any theoretically outliers either).

By this reason, using the rule of 1.5 IQR, you can see there aren't outliers in the displayed data set.

If you want to study more exercises using data sets, you can see this link https://brainly.com/question/16445367?referrer=searchResults

Answer:

The answer is 0

Step-by-step explanation:

It said it was right on khan!

Let A = {a, b, c, d}, B = {a, c, d, e}. Let f : A → R and g : B → R such that f = {(a, 1),(b, 2),(c, 2),(d, 4)} and g = {(a, 0),(c, 4),(d, 8),(e, 0)}. State the domain and find: f/g​

Answers

Answers:

Domain = {c, d}f/g = { (c, 1/2),  (d,  1/2) }

============================================================

Explanation:

The domain of f:  {a,b,c,d} which is drawn from set A.

The domain of g:  {a,c,d,e} which is drawn from set B

So far, we can see the possible inputs are: a,b,c,d,e

Let's go through each lowercase letter of the given sets

If 'a' is plugged into f/g, then we'll have 0 in the denominator due to the ordered pair (a,0) in function g. This causes a division by zero error so the input 'a' is not allowed in the domain of f/g.If we tried b, then it would work for function f, but it doesn't work for function g. If we tried to compute g(b), then the result is undefined. This is because the lowercase b input is not found in set uppercase B which is where function g selects its inputs from. So b is eliminated.The input c does work however. f(c) = 2 because of the ordered pair (c,2) in the function f. Similarly, g(c) = 4. This means f/g = 2/4 = 1/2 when the input is c. This shows that c is a valid input in the domain of f/g.The input d is pretty much the same story as input c. Moreover, the input d leads to the same output as c does. This time we have f/g = 4/8 = 1/2 when the input is d. Therefore, d is another valid input in the domain of f/g.The input e is not valid because (e,0) will lead to a division by zero error, as it's part of the g(x) function. So we must eliminate 'e' as a valid option in the domain. Even if we didn't have a division by zero error, we still have the fact that 'e' is not in the domain of the first function f. This is another reason why f/g is not defined when the input is 'e'.

To summarize, only inputs c and d are valid in the domain.

The domain is the set {c, d}

Both inputs in the domain lead to the output 1/2. This means the range of f/g is {1/2}. Despite having just one element inside, we must use curly braces to indicate we have a set.

The function f/g is { (c, 1/2),  (d, 1/2) }

We simply list all of the (x,y) ordered pairs to describe the function. In this case, there are only two such pairs.

Use the Distributive Property to multiply. 2(b – 7)

Answers

Answer:

2b - 14

Step-by-step explanation:

2(b – 7)

2b - 14

Answer:

[tex]2b-14[/tex]

Step-by-step explanation:

Using the distributive property, [tex]2(b-7)[/tex] can be written as [tex](2\cdot b)-(2\cdot7)[/tex] which solved/simplified is [tex]2b-14[/tex]

Man, it's late! Well, hope this helped you out and answered your question!

this isn’t a question but to everyone who’s actually good at math thank you so much for taking the time to answer these questions.

Answers

Answerurdsrd d e

Step-by-step explanation:

solve for x of the given angle ​

Answers

Answer:

m<ABC = 92

Step-by-step explanation:

(3x + 23) and 4x are equal angle wise. So we have the equation:

(3x + 23) = 4x

3x = 4x - 23

-x = -23

x = 23

Multiply x by 4 which is 92

185 for 4 tickets whats the price per ticket

Answers

46.25 according to my calculator
So 4 tickets cost $185. And we need to find the cost of each ticket. Take $185 divided by 4 and you get 46.25.
The cost of each ticket is $46.25.

A number is multiplied by 16, and that product is added to 4. The sum is equal to the product of 4 and 9. Find the number.

Answers

Answer:

The number is 2

Step-by-step explanation:

x * 16 + 4 = 9*4

x * 16 + 4 = 36

x * 16 + 4 - 4 = 36 - 4

x * 16 = 32

x * 16 / 16 = 32 / 16

x = 2

Answer:

The number is 2

Step-by-step explanation:

let the number be "a"

16a+4=4×9

16a+4=36

16a=36-4

16a=32

a=2

How many cubes of side 2cm can be fitted into a box 12 cm long, 8cm wide and 4cm high?

Answers

Answer:

there are 48cubes fetted into a box

The answer is 48.
You find the volume of the box - 12 X 8 X 4 = 384
Find the volume of the Cube with side 2 cm - 2 X 2 X 2 = 8
344 divided by 8 = 48
Therefore, 48 cubes would fit into the box

if SP is equal to rupees 400 and loss percent is 20% find CP​

Answers

SP=400Percentage of loss=20%

100-20=80%=400

[tex]\\ \rm\longmapsto 80\%\:of\:CP=400[/tex]

[tex]\\ \rm\longmapsto CP=400\times \dfrac{100}{80}[/tex]

[tex]\\ \rm\longmapsto CP=5(100)[/tex]

[tex]\\ \rm\longmapsto CP=500[/tex]

Step-by-step explanation:

Given,

S.p.=Rs400

Loss percent(L%) =20%

C.p.=?

We know,

S.p. =(100-L) % of c.p.

or,400=(100-20)% *c.p.

or,400=80% *c.p.

or, 400=80/100*c.p.

or,c.p.=Rs.500

Here, c.p.=Rs.500

A shop in the mall is 6 yards by 11 yards. How much would it cost to recarpet the shop with carpet that costs $5.00 per square yard?

Answers

Answer:

$330

Step-by-step explanation:

To find the total area of the shop do 6 times 11

6*11 = 66 sq. yards

Now, do 5 * 66 because one yard is $5

5 * 66 = 330

It costs $330

6 less than 8 times a number (x) is equal to 14

Answers

Answer:

8x-6=14

Step-by-step explanation:

Whenever you see less next to a number, you know it's gonna be -6. If it said 6 minus 8x though, then you would do 6-8x etc. Hope this helped.

Based on the table which college expenses would you consider fixed and which expenses would you consider variable? Why?

Answers

9514 1404 393

Answer:

fixed: tuition, room, mealsvariable: books, personal, transportation

Step-by-step explanation:

"Fixed" expenses are ones that don't change. They stay the same from year to year. Those would include ...

Fixed

tuition and fees: $4640room and board: $10,304campus meal plan: $3998

"Variable" expenses are ones that change depending on circumstances. Those would include ...

Variable

books and supplies: $1500 to 2500personal expenses: $3000 to 4600transportation: $0 to 800

PLEASE HELP NOW

write and solve an equation to find the value of X. please explain in details and show your work!

Answers

Answer:

Solution=96°+x+35°

=x+96°+35°

=x=96°-35°

=x=61°

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