Fabio and Gwen are saving money to buy a new gaming station. They need at least $510 to purchase the new gaming station. Gwen weeds yards and Fabio walks dogs to raise money. Gwen charges $12 each time she weeds a yard and Fabio charges $9 each time he walks a dog. The number of dog walks that Fabio has scheduled is no more than twice the number of yards Gwen has scheduled to weed. Fabio will walk at least 25 dogs. Write a set of constraints to model the problem, with x representing the number of lawns weeded and y representing the number of dogs walked.

Answers

Answer 1

Answer-

Set of constraints to model the problem are,

[tex]12x+9y\geq 510[/tex]

[tex]y \leq 2x[/tex]

[tex]y \geq 25[/tex]

Solution-

x = the number of lawns weeded by Gwen,

y = the number of dogs walked by Fabio.

1.

As, Gwen charges $12 each time she weeds a yard and Fabio charges $9 each time he walks a dog,

[tex]\text{Earnings of Gwen} = 12x[/tex]

[tex]\text{Earnings of Fabio} = 9y[/tex]

[tex]\text{Total earning} = 12x+9y[/tex]

They need at least $510 to purchase the new gaming station, means they need $510 or more than $510.

The equation for this is,

[tex]12x+9y\geq 510[/tex]

2.

The number of dog walks that Fabio has scheduled is no more than twice the number of yards Gwen has scheduled to weed, means

y must be less than or equal to 2x.

The equation for this is,

[tex]y \leq 2x[/tex]

3.

Fabio will walk at least 25 dogs, means y must be greater than of equal to 25.

The equation for this is,

[tex]y \geq 25[/tex]



Answer 2

Explanation:

Lets break the problem into steps and observe the constraints:

So Fabio and Gwen they are trying to save money and altogether they need at least $510.00.

Gwen charges $12.00 each time she weeds a yard.

Fabio charges $9.00 each time he walks a dog.

Fabio will walk at least 25 dogs. Here, 'x' represents the number of lawns weeded and 'y' represents the number of dogs walked.

Now talking about constraints:

Fabio will walk at least 25 dogs, so that implies:

[tex]y>25[/tex]

Also, the number of dog walks that Fabio has scheduled is no more than twice the number of yards Gwen has scheduled to weed, that implies:

[tex]y<2x[/tex]

The total money that they need after doing all the work should be at least $510.00.

[tex]12x+9y>510[/tex]



Related Questions

A veterinarian needs to know an animal's weight in kilograms if 20 lb is about 9 kg in a dog weighs 30 lb use a ratio table to find the dogs weigh in kilograms explain your reasoning

Answers

Answer:

13.5 kgs.

Step-by-step explanation:

Here we have to find conversion factor of lbs into kg.

For this we use the given information.

Given that the weight of a dog is 20 lbs and also 9 kg.

Hence we have conversion factor as

20 lbs = 9 kg

Or 1 lb =9/20 = 0.45 kg.

Using this, we find the 30 lb converted into kg.

For 1 lb, equivalent kg = 0.45

Hence for 30 lbs equivalent kg= 30(0.45) = 13.5 kg.


Miguel rode his bike 20 miles in 2.5 hours

Answers

Miguel rode his bike 20 miles in 2.5 hours

(1)Starting information is , In 2,5 hours Miguel traveled 20 miles

(2)Now we complete the table

In 2,5 hours distance traveled = 20 miles

So in 1 hour distance traveled = [tex]\frac{20}{2.5} =8 miles per hour[/tex]

Time             0   0.5       1         1.5       2        2.5

Distance       0    4         8         12       16         20

(3) The graph is attached below

(4) Equation y = kx

y is the distance

x is the time

Distance = k (time)

We know speed is 8 miles per hour

So k is 8

y = 8k is the final equation

(5) k is the constant of proportionality

the value of k= 8

so 8 is the constant of proportionality.

Answer:

Step-by-step explanation:

1). Miguel rode his bike 20 miles in 2.5 hours.

2). Since Miguel rode his bike with the speed = [tex]\frac{20}{2.5}=8[/tex] miles per hour

So the table will be

Time          0       0.5      1       1.5        2       2.5

Distance    0        4        8       12       16       20    

3). Graph for the given equation is attached.

4). Since y = kx represents the situation then for Distance y = 4 miles in time x = 0.5 hours

4 = k(0.5)

k = [tex]\frac{4}{0.5}=8[/tex]

Therefore, equation will be y = 8x.

5). Since y = kx

⇒ k = [tex]\frac{y}{x}[/tex]

Proportionality constant k represents the speed of Migual.

Solve the equality, - (7c-18)-2c>0

Answers

(7c-18)-2c>0

group like terms: 7c-2c-18>0

add similar elements: 7c-2c=5c
5c-18+18>0+18

Add 18 to both sides
5c-18+18>0+18

simplify
5c>18

divide both sides by 5
5c÷5>18/5

simplify
c>18/5



Which sequence of similar transformations could map △ABC onto △A'B'C'?


dilation and reflection

dilation and translation

translation and rotation

translation and reflection

Answers

A dilation and a translation could have occurred to map [tex]{\Delta \;\text{ABC}}[/tex] to [tex]{\Delta \;\text{A''B''C''}}.[/tex]

Further Explanation:

Given:

The options are as follows,

(A). A dilation and a reflection

(B). A dilation and a translation

(C). A translation and a rotation

(D). A translation and a reflection

Explanation:

The reflection symmetry is defined as a line that divides the Figure into two equal parts.

Translation can be defined as to move the function to a certain displacement.

Rotation is defined as a movement around its own axis. A circular movement is a rotation.

A dilation and a translation could have occurred to map [tex]{\Delta \;\text{ABC}}[/tex] to [tex]{\Delta\; \text{A''B''C''}}.[/tex]

Option (a) is not correct.

Option (b) is correct.

Option (c) is not correct.

Option (d) is not correct.

Learn more:

If the clothing maker bought 500 m2 of this fabric, how much money did he lose? use 1tepiz=0.625dollar and 0.9144m=1yard https://brainly.com/question/2479097.Suppose that you find the volume of all the oceans to be 1.4×109km3 in a reference book. to find the mass, you can use the density of water, also found in this reference book, but first you must convert the volume to cubic meters. what is this volume in cubic meters? https://brainly.com/question/1446243.

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Geometry

Keywords: sequence, similar, Transformation, reflection, dilation, rotation, translation, rigid, motion, rigid motions.

which values are possible rational roots of 9x3+14x2−x+18=0 according to the rational root theorem

+-1/3
+-1/8
+-3
+-1/2

Answers

ANSWER

The possible rational roots are
[tex] \pm \frac{1}{3} [/tex]
and

[tex] \pm \: 3[/tex]

EXPLANATION

According to the rational root theorem,

All factors of the constant term expressed over each factor of the coefficient of the highest degree of the polynomial are all possible rational roots.

The factors of 18 are:

[tex] \pm1, \: \pm2, \pm3, \pm6, \pm9, \pm18,[/tex]

and the factors of 9 are:

[tex] \pm1, \pm3, \pm9,[/tex]

Out of the possible ratios we get the options

[tex] \pm\frac{ 1}{3} [/tex]
and .
[tex] \pm \: 3 [/tex]
Final answer:

According to the Rational Root Theorem, the potential rational roots of the equation 9x^3 + 14x^2 - x + 18 = 0 are ±1/3 and ±3. The values ±1/8 and ±1/2 are not valid since their denominators are not factors of the leading coefficient, which is 9.

Explanation:

The possible rational roots of the polynomial equation 9x^3 + 14x^2 - x + 18 = 0 can be determined using the Rational Root Theorem. This theorem states that any rational solution, expressed in the form of a fraction p/q, where p is a factor of the constant term and q is a factor of the leading coefficient, must be among these possible roots.

The constant term in this equation is 18, and its factors are ±1, ±2, ±3, ±6, ±9, ±18. The leading coefficient is 9, with factors of ±1, ±3, ±9. According to the Rational Root Theorem, we take each factor of the constant term and divide by each factor of the leading coefficient to find the possible rational roots. Thus, the potential rational roots are ±1/1, ±1/3, ±1/9, ±2/1, ±2/3, ±2/9, ±3/1, ±3/3, ±3/9, and so forth, including their negative counterparts.

From the options provided in the question, the potential rational roots that fit the criteria set by the theorem are: ±1/3, and ±3. The other options, ±1/8, ±1/2, do not satisfy the theorem as their denominators are not factors of the leading coefficient.

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An angle is formed by:

A. any ray and any line
B. parallel lines
C. any two rays
D. two rays that share the same endpoint

Answers

The answer is choice D) Two rays that share the same endpoint

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

Here's a full breakdown of the four choices

A. False. If the ray and line aren't touching, then an angle can't be formed.

B. False. Parallel lines never cross. The same issue as before (in part A) comes up.

C. False. Again the rays need to meet up somehow.

D. True. If you have two rays that share the same endpoint, then they form an angle. Think of it like a pair of scissors. Each blade is a ray. The blades are joined at a common node to allow the blades to swing open or closed. You could have an angle formed by line segments or lines, but they would have to intersect in some way.

Option D. two rays that share the same endpoint, is correct.

An angle is formed by:
A. any ray and any line
B. parallel lines
C. any two rays
D. two rays that share the same endpoint

What is angle?

The angle can be defined as the one line inclined over other line.

When the line as same end points and
one of the line is inclined over other by some measure called as angle.

Thus the option D two rays that share the same endpoint is correct

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The graph shows the amount of money Miguel earns after working x hours

Answers

Answer:

13

Step-by-step explanation:


Answer:

D

Step-by-step explanation:

trust

−4 4/5 ÷ 4 A.​ −1 1/5 ​ ​​ B. −4/5 C. 4/5 ​​ D. 1 1/5

Answers

Answer:

A. -1 1/5

Step-by-step explanation:

−4 4/5 ÷ 4 = -1.2

-1.2 as a fraction would be, -1 1/5


Hope this helps :-)

7.5x+20y=900 models how many hours (x) and how many lawns mowed (y) Jon has to work in order to save $900. Give 3 combinations of hours worked and lawns mowed that result in $900.

Answers

Final answer:

The equation 7.5x + 20y = 900 can be solved for y by substituting different values for x to find three combinations that satisfy the equation: (0 hours, 45 lawns), (40 hours, 30 lawns), and (80 hours, 15 lawns).

Explanation:

The equation 7.5x + 20y = 900 models the relationship between the hours worked (x) and lawns mowed (y) for Jon to save up $900. To find combinations that result in $900, we can select different values for x or y and solve for the other variable.

Let x = 0 (no hours worked), then 7.5(0) + 20y = 900, which simplifies to 20y = 900. Dividing both sides by 20 gives us y = 45. So, one combination is (0 hours, 45 lawns).Let x = 40 (hours worked), then 7.5(40) + 20y = 900, which simplifies to 300 + 20y = 900. Subtracting 300 from both sides gives us 20y = 600, and dividing by 20 results in y = 30. Thus, another combination is (40 hours, 30 lawns).Let x = 80 (hours worked), then 7.5(80) + 20y = 900, which simplifies to 600 + 20y = 900. Subtracting 600 from both sides gives us 20y = 300, and dividing by 20 results in y = 15. Therefore, a third combination is (80 hours, 15 lawns).

These three combinations represent different ways Jon can work hours and mow lawns to reach his goal of saving $900.

max and his friend eke are comparing their ages. They figure out that if they double max's age from 3 years ago and add it to zee's current age, the sum is 26.If zeke is currently 8 years old determine how old max currently is.

Answers

Answer:

Max is currently 12 years old.

Step-by-step explanation:

Zeke's current age = 8 years

Lets take Max's current age as [tex]x[/tex] years.

Then Max's age 3 years ago = [tex]x-3[/tex]

Double Max's age 3 years ago = [tex]2*(x-3)[/tex]

Double Max's age 3 years ago + Zee's current age = 26

⇒ [tex]2*(x-3)[/tex] + [tex]8[/tex] = [tex]26[/tex]

=[tex]2*(x-3)+8=26[/tex]

=[tex]2x-6+8=26[/tex] (Simplifying the brackets)

=[tex]2x+2=26[/tex]

=[tex]2x+2-2=26-2[/tex][tex]2x=24

=[/tex][tex]x=12[/tex]

So Max's current age is 12 years.


Mr. James deposits $450,000 at the end of each year for 10 years. What will be the value of his money at the end of 10 years at (a) 9%, (b) 10% and (c) 12%?

Answers

A. 405,000

B. 450,000

C. 540,000

Two triangular pyramids are similar. The volume of the larger pyramid is 729 cm3 , and the volume of the smaller pyramid is 64 cm3. If the perimeter of the base of the smaller pyramid is 8 cm, what is the perimeter of the base of the larger pyramid? 18 cm 18 cm2 27 cm 27 cm2

Answers

Answer:

It's the first option

Step-by-step explanation:

I just answered the question on edge

Final answer:

The perimeter of the base of the larger pyramid is 12 cm, determined through the ratio of the volumes of the pyramids.

Explanation:

The volumes of similar figures are related by the cube of the ratio of their corresponding lengths. If the larger pyramid has a volume of 729 cm³ and the smaller pyramid has a volume of 64 cm³, then the ratio of their volumes is 729/64, which is the cube of the ratio of their corresponding lengths. Taking the cube root of this ratio gives 3/2, so the lengths in the larger pyramid are 3/2 times the lengths in the smaller pyramid. Thus, if the perimeter of the base of the smaller pyramid is 8 cm, the perimeter of the base of the larger pyramid is 3/2 times this, or 12 cm.

Learn more about Pyramids here:

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For the piecewise Function below, which of the following statments is true? Someone please help me

Answers

The first one and the third one are correct. because for the when you plug 1 on the first piece wise function you get 3.

f(3) =1. and f(1)=3 so f(1)>f(3)

Remark

Let's just figure out what f(1) and f(3) are and what equation to use.

f(1)

f(1) is defined by the top condition. Look at the condition carefully. -3 ≤ x ≤ 1

So the value of f(1) is

(x + 1)² -1

(1 + 1)² - 1

2² - 1

4 - 1 = 3

f(3)

f(3)  is governed by the middle condition. 1 < x ≤ 3

The value of f(3) is  - x + 2 = - 3 + 2 = - 1

Conclusion

f(1) > f(3)

Comment

Both f(1) and f(3) are defined. You just have to look around to find out where. D is wrong.

We calculated both f(1) and f(3). f(1) is larger than f(3)  so that is your answer.

Help! Geometry question.

Answers

Start with congruencies of 130°:

∠1 and 130° are vertical angles

∠2 and 130° are corresponding angles

∠5 and 130° are alternate exterior angles

m∠1 = m∠2 = m∠5 = 130°

∠7 and 130° are supplementary angles (which means their sum is 180°). So, ∠7 = 50°

Next, find congruencies of ∠7:

∠3 and ∠7 are vertical angles

∠4 and ∠7 are corresponding angles

∠6 and ∠7 are alternate exterior angles

m∠3 = m∠4 = m∠6 = m∠7 = 50°

Answer: B



Solve these equations:
1. 2(n+1)+1=(n-5)+(n-2)
2. 3(n-1)-2=4(n-4)-(n-1)

Answers

Hey there!!

First equation :

Given equation :

... 2 ( n + 1 ) + 1 = ( n - 5 ) + ( n - 2 )

Excluding the parenthesis and using the distributive property :

... 2n + 2 + 1 = n - 5 + n - 2

Combining all the like terms on each side :

... 2n + 3 = 2n - 7

Subtracting 2n and subtracting 3 on both sides :

... 0 = -10

Hence, the first equation has "zero" values.

Second equation :

Given equation :

... 3 ( n - 1 ) - 2 = 4 ( n - 4 ) - ( n - 1 )

Using the distributive property :

... 3n - 3 - 2 = 4n - 16 - n + 1

Combining all the like terms :

... 3n - 5 = 3n - 15

Adding 5 and subtracting 3n on both sides :

... 0 = -10

Hence, the second equation has "zero" values.

Hope my answer helps!!

Hope this helps. Good luck

Find the measure of z.

A. 80°
B. 83 °
C. 70 °
D. 87 °

Answers

z and 100 are on the same line so the total is 180

180-100=z

80=z

Please give Brianest

200 = 16(6t - 13)

t = ?
Help!

Answers

Step 1. Divide both side by 16

100/16 = 6t - 13

Step 2. Dimplify 200/16 to 25/2

25/2 = 6t - 13

Step 3. Add 13 to both sides

25/2 + 13 = 6t

Step 4. Simplify 25/2 + 13 to 51/2

51/2 = 6t

Step 5. Divide both sides by 6

51/2/6 = t

Step 6. Simplify 51/2/6 to 51/2 * 6

51/2 * 6 = t

Step 7. Simplify 2 * 6 to 12

51/12 = t

Step 8. Simplify 51/12 to 17/4

17/4 = t

Step 9. Switch sides

t = 17/4

Here's what you have to do.


You see "16(6t-13)"

Mupilty 16 and 13 and get 208.

Divide 208 by 6 and you will get 34.6 Reapeting. That's your answer

Timmy writes the equation f(x) = 1/4x – 1. He then doubles both of the terms on the right side to create the equation g(x) = 1/2x – 2. How does the graph of g(x) compare to the graph of f(x)? The line of g(x) is steeper and has a higher y-intercept. The line of g(x) is less steep and has a lower y-intercept. The line of g(x) is steeper and has a lower y-intercept. The line of g(x) is less steep and has a higher y-intercept.

Answers

Remark

The best way to answer something like this is to actually graph both equations. I have done that for you below.

Red Line: f(x) = 1/4x - 1

Blue Line: g(x) = 1/2x - 2

Now look at the answers.

A: The first one is incorrect. You don't need the graph to tell you that. The larger the number in front of the x, the steeper the line. Put another way, the larger the slope, the steeper the line. The y intercept is lower however.

B is wrong. g(x) is steeper, but the y intercept is lower not higher than f(x) [Negatives do strange things].

C:The g(x) is steeper (we've said that a couple of times), and it has a lower y intercept.

D is correct.

E is just wrong. Both parts are incorrect.


A 6.7 kg object moves with a velocity of 8 m/s . What it’s kinetic energy ?

Answers

214.4J (Joules) Kinetic energy= 1/2 *m*v^2 with Kinetic energy = 1/2* 6.7* 8 *8 = 214.4J.

Answer:

The Correct answer to this question for Penn Foster Students is: 214.4 J

Step-by-step explanation:


5j+s=t-2 solve for t

Answers

The answer is

T= 5j+s+2


t=5j+s+2. Your answer should be: t=5j+s+2.

Let's solve for t.

5j+s=t−2

Step 1: Flip the equation.

t−2=5j+s

Step 2: Add 2 to both sides.

t−2+2=5j+s+2

t=5j+s+2

What numbers are 3 units away from -1 on a number line?

Answers

Answer: 2 and -4

Step-by-step explanation:

tiffanyrenaew21 is not completely right. The correct answer would be 2 and -4. This is how you find your answer:

First you form an equation: |x-(-1)|=3

|x+1|=3 - - - - - - - - |x+1|=-3

Subtract 1 from both sides

x=2 - - - - - - - - - - x=-4

You will always have 2 answers as absolute value equations and inequalities can always be positive or negative. |positive or negative| = positive.

If |x|=-n, then there are no solutions, becuase absolute value can't be negative.

Frances has piano lessons every fourth day.
She has ballet lessons every fifth day.
She has soccer every second day.
On which day will she first have all three activities?
Explain how you know.

Answers

Final answer:

Frances will first have piano lessons, ballet lessons, and soccer on the 20th day as it is the least common multiple of the days she has each activity (4, 5, and 2 days respectively).

Explanation:

The student is asking about the day Frances will first have piano, ballet, and soccer activities all on the same day. This calls for finding the least common multiple (LCM) of the numbers representing the days on which she has each activity (every fourth, fifth, and second day).

Frances has piano lessons every fourth day, ballet every fifth day, and soccer every second day. To find the day when all three activities coincide, we need to calculate the LCM of 4, 5, and 2:

The multiples of 4 are 4, 8, 12, 16, 20, 24,...The multiples of 5 are 5, 10, 15, 20, 25,...The multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20,...

The first common multiple they all share is 20. Therefore, Frances will first have all three activities on the 20th day.

The rectangle below has a total perimeter of 190 in:

rectangle with width of 4

Which of the following equations can be used to determine the length of the longer side of the rectangle?
x + 4 = 190
4x = 190
2x + 8 = 190
16x = 190

Answers

Answer would be 2x + 8 = 190

Let

x-------> the length of the rectangle

y------> the width of the rectangle

we know that

the perimeter of the rectangle is equal to

[tex]P=2x+2y[/tex]

[tex]P=190\ in[/tex]

so

[tex]2x+2y=190[/tex]------> equation A

[tex]y=4\ in[/tex] ------> equation B

substitute equation B in equation A

[tex]2x+2*4=190[/tex]

[tex]2x+8=190[/tex]

therefore

the answer is

[tex]2x+8=190[/tex]


The table shows the rates at which Ajay and Tory are biking along the same trail.

Person: Rate:
Ajay: 200
Tory: 250

a. Suppose Ajay began the trail 325 meters ahead of Tory. Write a system of equations to represent the distance y each person will travel after any number of mimutes x.

Answers

Answer:

For Ajay , [tex]y=200x+325[/tex]

For Tory, [tex]y=250x[/tex]

Step-by-step explanation:

Formula to find distance = rate × time

Rate of Ajay = 200

Rate of Tory = 250

In x minutes

Distance travelled by Ajay = 200 ×x = 200x

Distance travelled by Tory = 250 ×x = 250x

But Ajay was already ahead by 350 meters.

So for Ajay, the distance y traveled in x minutes

[tex]y=200x+375[/tex]

For Tory

[tex]y=250x[/tex]


Answer:

The rates are:

Ajay : 200

Tory : 250

I assume those are in meters per minute.

Now, we suppose that Ajay began the trail 325 meters ahead, so if we put the zero in Tory position, we got:

Ajay position = 325 meters + 200*x meters

Tory position = 250*x meters

Where x is the number of minutes after they started to bike.

From this, we can compare their positions, and see in which minute x Tory position and Ajay position are the same.

325 + 200x = 250x

325 = 250x - 200x = 50x

x = 325/50 = 6.5 minutes.

So before of x = 6.5 minutes, Ajay is ahead. After x =6,5 minutes, Tory is ahead.

I need help please!!

Answers

the first answer is correct


[tex]x + y = 3[/tex]

two cousin one is five years older. the sum of there age is 37. how old are they

Answers

Subtract the difference from the total, then divide by 2, that would be the age of the youngest, then add the difference to that for the age of the oldest.



37 - 5 = 32

32 / 2 = 16

The youngest is 16.


16 + 5 = 21

The oldest is 21.


The ages are 16 and 21.


51 is the product of diego’s score and 3

Translate into an equation

Answers

Answer:

3d = 51 is the desired equation; its solution is d = 17.

Step-by-step explanation:

Let d represent Diego's score.  Then 3d = 51, or d = 17.


"51 is the product of Diego's score and 3" is written as 51=3x. We know this because "is" means "=", and "the product of" means multiplication. Since "Diego's score" is unknown, it would be a number x (multiplied by 3 would make it 3x). The answer to this is 17, because 51/3=17. :)

Combine the like terms to create an equivalent expression:
−2x − x + 8
Will Mark Brainliest!

Answers

Answer:

-3x+8

Step-by-step explanation:

-x is the same as -1x

-2x plus -x is 3x

8 stays the same

if (x) = 7 -x , find f(3)

Answers

f(3) means you replace x with 3.


f(x) = 7-x

f(3) = 7-3

f(3) = 4

Hey there!!

Given :

f( x ) = 7 - x

What is f(x)?

f(x) is basically the y.

The question states :

y = 7 - x

Now, find ( 3 )

This states that, I have given the value for x and find y.

y = 7 - x

y = 7 - 3

y = 4

Hence, f(3) = 4

Hope helps!

What is the justification for each step in the solution of the equation?

23x−13=2(x+2)

Select from the drop-down menus to correctly justify each step.

HEEEEELLLPPP!!!!!!

Answers

23x-13=2(x+2)

First you would distribute the 2 into the parenthesis

It will look like this after: 23x-13=2x+4

Then you would subtract 2x on both sides because u have to get the x's on one side

It will look like this after:21x-13=4

Then you would add 13 to both sides

It will look like this after: 21x=17

Then you would divide 21 on both sides

Your final product is 21/17


The solution to the equation 23x - 13 = 2(x + 2) is found by distributing, subtracting 2x, adding 13, dividing by 21, and then checking the solution.

To solve the algebraic equation 23x - 13 = 2(x + 2), let's apply algebraic methods and justify each step:

Distribute the 2 into the parentheses on the right side of the equation: 23x - 13 = 2x + 4. This step applies the distributive property a(b + c) = ab + ac.

Subtract 2x from both sides to start isolating x: 21x - 13 = 4. This maintains the balance of the equation, following the subtraction property of equality.

Add 13 to both sides in order to get terms with x on one side and constants on the other: 21x = 17. This action uses the addition property of equality.

Divide both sides by 21 to solve for x: x = 17/21. This is done using the division property of equality to isolate the variable x.

Check the solution by substituting x back into the original equation to ensure that both sides are equal.

By following these steps, we arrive at the correct solution for x and justify the use of algebraic properties that ensure the balance and equivalence of the equation throughout the process.

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