Algebra Word Problem

Hello, everyone. I really need for someone to confirm or deny that I have solved this algebraic word problem correctly. I do not have very much confidence in my math skills, so even when I DO get the right answers, I need someone to reaffirm it. Thank you in advance. Here's the question:

"Twice the difference of a number and 3 is equal to the quotient of 48 and 4. Find the number".

My answer is: x=9. Whether or not I am correct, can someone please break down the equation solving for me?

thanks again....Kaydee College Student Mom

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Algebra Word Problem

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Aug 24, 2010
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by: Karin

Yes, technically you are correct! Unfortunately in all my years teaching math, textbooks never translate it this way. So, I've conditioned myself over the years to follow the curriculum and text books.

However, this problem should technically be written as an absolute value equation because the difference between any two numbers is always positive.

Think about it: If I say, "What is the difference between 4 and 3?", you would say 1. If I say, "What is the difference between 3 and 4?", you would say 1, not -1. In the context of a real problem, the difference usually means how many units between the two numbers?

Therefore, this equation, technically should be written as:

2|x-3| = 12

This would then result in an answer of x = 9 or x = -3.

(This is more of an Algebra 2 or Intermediate Algebra skill.)

Thank you for bringing me out of my textbook world!
Aug 24, 2010
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starstarstarstarstar 		another answer
by: http://keepingmathsimple.wordpress.com

in my previous comment, i have the numberline in mind. the difference could be interpreted as the distance between the two numbers hence taken as positive.
Aug 24, 2010
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by: http://keepingmathsimple.wordpress.com

I believe there is another answer: x = -3.
It's because of the word difference. The difference between x and y could mean x-y or y-x.
Aug 20, 2010
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starstarstarstarstar 		Thank You!
by: Anonymous

Karin,

Thank you soooo much. I label myself the math idiot, but lately, I've been solving some difficult problems correctly and I'm not as terrified of math as I once was.
Aug 20, 2010
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by: Karin

Thank you for submitting your word problem. I hope that you have more confidence in yourself, because your answer is correct!

That's one of the best things about math - you can usually check your answer to make sure that it is correct.

Here's a step by step break down of the problem.

Twice the difference of a number and 3
2(x-3) Remember that difference means
subtract and since we don't know the
number, we'll use a variable.

Equals the quotient of 48 and 4.
2(x-3) = 48/4 Quotient means divide

Now we can solve:

2(x-3) = 12 48/4 = 12
2x-6 = 12 Use the distributive prop.
2x-6+6 = 12+6 Add 6 to both sides
2x = 18 12+6=18
2x/2 = 18/2 Divide by 2 on both sides
x = 9 18/2=9


Then you can check:

2(9-3) = 12
2(6) = 12
12=12

I hope this helps and I hope that you gain confidence in your math ability!

Karin

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