Given the equation 5x − 4 = –2(3x + 2), solve for the variable. Explain each step and justify your process. B. Megan solved a similar equation below. Is Megan's solution correct? Explain why or why not. 3(2x − 4) = 5x − 1 6x − 12 = 5x − 1 11x − 12 = –1 11x = 11 x = 11

QUESTION POSTED AT 03/12/2019 - 10:29 AM

Answered by admin AT 03/12/2019 - 10:29 AM

A.
5x-4=-2(3x+2) \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\
5x-4=-2 \times 3x-2 \times 2 \\
5x-4=-6x-4 \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 6x to both sides} \\
11x-4=-4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 4 to both sides} \\
11x=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{divide both sides by 11} \\
x=0

B.
3(2x-4)=5x-1 \\
6x-12=5x-1 \\
\boxed{11x-12=-1} \Leftarrow \hbox{the first mistake} \\
11x=11 \\
\boxed{x=11} \Leftarrow \hbox{the second mistake}

Megan's solution isn't correct.
The first mistake: she subtracted 5x from the right-hand side of the equation, but added 5x to the left-hand side.
The second mistake: she divided the right-hand side of the equation by 11, but didn't divide the left-hand side.

The correct solution:
3(2x-4)=5x-1 \ \ \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\
3 \times 2x+3 \times (-4)=5x-1 \\ 6x-12=5x-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{subtract 5x from both sides} \\
x-12=-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  |\hbox{add 12 to both sides} \\
x=11
Post your answer

Related questions

A survey found that 12 out of every 15 people in the United states prefer eating at a restaurant over cooking at home. if 400 people selected eating at a restaurant on the survey, how many people took the survey...

On a certain survey it says:
12 out 15 people in the United States prefer eating at the restaurant rather than home.
To know how many percent is this.
=> 12 / 15
=> 0.8 which is also 80%
Now, the  80% of the those people in the survey is 400.
Find the total number  of people who took the survey.
Since we already have the 80%, we need to find the number of 20%
=> 400 x 20%
=> 400 x .20
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=> 400 + 80
=> 480 => the total number of people who took the survey





ANSWERED AT 09/12/2019 - 05:12 AM


QUESTION POSTED AT 09/12/2019 - 05:12 AM

What is 24 tenths - 1 one 3 thenths

240-31=209 is the answer i belive

ANSWERED AT 09/12/2019 - 05:12 AM


QUESTION POSTED AT 09/12/2019 - 05:12 AM

How do you solve 5v-4 over 10 equals 4/5

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Next, you add four to each side, getting 5v = 8+4 or 5v = 12.

Finally, you divide each side by 5. The answer is: v = 12/5

ANSWERED AT 09/12/2019 - 05:12 AM


QUESTION POSTED AT 09/12/2019 - 05:12 AM

What two numbers add to 4 and multiply to 1

There are no numbers for this, thus you will have to use the quadratic formula.

ANSWERED AT 09/12/2019 - 05:12 AM


QUESTION POSTED AT 09/12/2019 - 05:12 AM

At the bake sale connie bought 4 chocolate cookies kevin bought 4 brownies and luis bought 6 sugar cookies in simplest form what fraction represents the number of cookies bought

3/7 is the correct awnser as u can see because connie has 4 choclate cookies and kevien bought 4 brownies and luis bought 6 sugar cookies and in the simplest form the fraction would be 3/7.

ANSWERED AT 09/12/2019 - 05:11 AM


QUESTION POSTED AT 09/12/2019 - 05:11 AM

What adds up to 11 and multiples to -60?

The answer you seek is 15 and -4. 15*-4=-60 and 15-4=11.

ANSWERED AT 09/12/2019 - 05:10 AM


QUESTION POSTED AT 09/12/2019 - 05:10 AM

Use compatible number to find two estimate 2,242÷33

Compatible numbers are also considered as estimates numbers.
Now the given equation is 2 242 / 33
=> Let’s find the compatible number to find the estimate quotient
=> 2 242 – 2 = 2 240
=> 33 + 2 = 35
=> 2 240 / 35
=> 62, this is the estimated quotient
The correct answer is:
=> 2 242 / 33
=> 67.94, the exact answer.
62 and 67.94 is not exactly the same but close. That’s how estimation works.



ANSWERED AT 09/12/2019 - 05:09 AM


QUESTION POSTED AT 09/12/2019 - 05:09 AM

Greensboro gets 12 times as many inches of snow as Redville gets. Altoghter, the two towns gets 65 inches of snow.How many inches of snow does redville get?

Inches of snow Greensboro gets = g
Inches of snow Redville gets = r

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Redville gets 5 inches of snow.

ANSWERED AT 09/12/2019 - 05:08 AM


QUESTION POSTED AT 09/12/2019 - 05:08 AM

Two numbers that add up to 18 and multiplied equals 11

These numbers are 9 and 2. 9*2=18 and 9+2=11.

ANSWERED AT 09/12/2019 - 05:07 AM


QUESTION POSTED AT 09/12/2019 - 05:07 AM

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ANSWERED AT 09/12/2019 - 05:06 AM


QUESTION POSTED AT 09/12/2019 - 05:06 AM

If Yvonne wanted to make 3 dresses that use 4 7/8 yd of fabric each, explain how she could use estimation to make sure she has enough fabric for all of them

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ANSWERED AT 09/12/2019 - 05:06 AM


QUESTION POSTED AT 09/12/2019 - 05:06 AM

Two students participated in a fund-raiser. Each sold a combination of pencils and notebooks. The first student sold 2 pencils and 8 notebooks for a total of $17. The second student sold 10 pencils and 3 notebooks for a total of $11. Find the price of each item. Write a system of equations (two equations), and define the variables also. x= y= 1) 2)9 POINTS! Please help!

2x + 8y = 17
10x + 3y = 11

We need to solve the system of equations.

x = pencils
y = notebooks

If we solve by graphing, we get the answer:

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ANSWERED AT 09/12/2019 - 05:05 AM


QUESTION POSTED AT 09/12/2019 - 05:05 AM

What is a type expression that contains a variable or variables

An expression for a type of proportionality so like y=kx where y is dependent and x is independent and the y and x will be the variables while k is constant of proportionality This can also be stated k=y/x so to find k you divide dependent by independent Don't confuse this with science trust me you don't wanna do the y/x in science

ANSWERED AT 09/12/2019 - 05:03 AM


QUESTION POSTED AT 09/12/2019 - 05:03 AM

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ANSWERED AT 09/12/2019 - 05:01 AM


QUESTION POSTED AT 09/12/2019 - 05:01 AM

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ANSWERED AT 09/12/2019 - 05:00 AM


QUESTION POSTED AT 09/12/2019 - 05:00 AM

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ANSWERED AT 09/12/2019 - 04:59 AM


QUESTION POSTED AT 09/12/2019 - 04:59 AM

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ANSWERED AT 09/12/2019 - 04:58 AM


QUESTION POSTED AT 09/12/2019 - 04:58 AM

Explain how knowing 1+7 helps you find the sum for 7+1

Knowing 1+7 helps you find the sum of 7+1 because 1+7 and 7+1 is communitive property of addition. Also because 1+7 is the same answer as 7+1. 
Ex:
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ANSWERED AT 09/12/2019 - 04:58 AM


QUESTION POSTED AT 09/12/2019 - 04:58 AM

Please solve for n and show your work. (n+15)=-2

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First, replace the numerator with the parentheses.
 \frac{n+15}{3} =-2
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n + 15 = -2 * 3
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n + 15 = -6
Fourth, take away 15 from each side.
n = -6 - 15
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Answer: n = -21

ANSWERED AT 09/12/2019 - 04:57 AM


QUESTION POSTED AT 09/12/2019 - 04:57 AM

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Find how many liters of strawberries are there in 400 kilograms.
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=> to check if our answer is correct.
To this formula
=> answer x divisor
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ANSWERED AT 09/12/2019 - 04:57 AM


QUESTION POSTED AT 09/12/2019 - 04:57 AM

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I got the answer is 2%. i hope that's the answere 

ANSWERED AT 09/12/2019 - 04:57 AM


QUESTION POSTED AT 09/12/2019 - 04:57 AM

What is $29000; 4% decrease

29000 x 0.04 = 1,160
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ur welcome :) be friends with me if you want me to help you in the future :)

ANSWERED AT 09/12/2019 - 04:56 AM


QUESTION POSTED AT 09/12/2019 - 04:56 AM

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ANSWERED AT 09/12/2019 - 04:54 AM


QUESTION POSTED AT 09/12/2019 - 04:54 AM

What is the solution of the equation x+6 divided by 2 equals 5

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ANSWERED AT 09/12/2019 - 04:54 AM


QUESTION POSTED AT 09/12/2019 - 04:54 AM

Solve these word problems 1---3 1: A factory processes 1,560 ounces of olive oil per hour. The oil packaged into 24-ounces bottles.How many bottles does the factory fill in one hour 2: A pond at a hotel holds 4,290 gallons of water.The groundskeeper drains the pound at a rate of 78 gallons of water per hour.How long will it take to drain the pound? 3:Explain using partial quotients to divide is similar to using the Distributive proprerty to multiply

1. To do this, you want to divide 1560 by 24.  This gives you 65.  The bottle fills 65 bottles per hour.
2. To do this divide 4290 by 78.  The result is 55.  It would take the groundskeeper 55 hours to drain the pond.  
3. They are similar because you break up pieces of the number and then you combine them.

ANSWERED AT 09/12/2019 - 04:53 AM


QUESTION POSTED AT 09/12/2019 - 04:53 AM

What is 4y=3x 12 in slope intercept form

Slope intercept form i.e. y = mx + b
   4y = 3x + 12
    y = 3/4x + 3 Ans

ANSWERED AT 09/12/2019 - 04:53 AM


QUESTION POSTED AT 09/12/2019 - 04:53 AM

The area of a mirror is 225 square inches, and its width is 13 3/4 inches. Will the mirror fit in a space that is 15 inches by 16 inches? Explain

If you multiply length times width to get area, it's the same with division. You do area divided by length or width. The equation would be 225 divided by 13 3/4. 225/13 3/4= 16.36 inches. 16.36 > 16 inches, so the answer would be no. (The mirrors length and width are 13 3/4 inches by 16 9/25)

ANSWERED AT 09/12/2019 - 04:53 AM


QUESTION POSTED AT 09/12/2019 - 04:53 AM

What is the value of 4 in 6.54

The 4 in that number is in the hundredths section. It means the 4 represents four hundredths.

ANSWERED AT 09/12/2019 - 04:52 AM


QUESTION POSTED AT 09/12/2019 - 04:52 AM

What is the solution on a 10×10 grid for 0.8 × 0.4

You know how the grid is right? Well shade in 40 (0.4) boxes across. Then shade 80 (0.8) boxes down. Hope this helped

ANSWERED AT 09/12/2019 - 04:51 AM


QUESTION POSTED AT 09/12/2019 - 04:51 AM

Can you show how to solve this question? Thomas and Sharlina work on weekends and holidays doing odd jobs around the neighborhood. They are paid by the day, not by the hour. They each earn the same whole number of dollars per day. Last month Thomas earned $184 and Sharlina earned $207 a. How many days did each person work? b. Whatis their daily pay PLEASE EXPLAIN HOW YOU GOT YOUR ANSWER

To find out how much they earned, we need to find the GCF of 184 and 207.

The greatest common factor (GCF) of 184 and 207 is 23.

That means they earn 23 dollars per day. That is your answer for part b.

And Thomas worked 184/23 = 8 days
While Sharlina worked 207/23 = 9 days

That is your answer for part a.

ANSWERED AT 09/12/2019 - 04:51 AM


QUESTION POSTED AT 09/12/2019 - 04:51 AM