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# Algebra Equation with Fractions

The answer is x=-3. Where am I going wrong? Thanks.

4x/6 - x+5/2 = 6x-6/8

24(4x/6) - 24(x+5/2) = (6x-6/8)24

4(4x) - 12(x+5) = (6x-6)3

16x - 12x-60 = 18x-18

4x-60 = 18x-18
-4x          -4x

-60 = 12x-18
+18 =      +18

-42/12 = 12x/12

-7/2 = x
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2 Solutions

Commented:
Right part of the third line doesn't seem right.
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Commented:
(6x-6/8)24 does not = (6x-6)3

Looks like you tried pulling a  /8  out of there and applied it to the 24.

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Commented:
... and neither does the left part of the third line.
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Commented:
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Author Commented:
I found the LCD of 6,2 and 8 = 24
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Author Commented:
What's wrong with it?

24/6=4  24/2=12  24/8=3
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Commented:

The left side of line 2

24(4x/6) - 24(x+5/2)

could be rewritten as

24 (   (4x/6)-(x+5/2)  )

Which leads to both sides getting  /24 , so the 24 would disappear.
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Commented:
Ignore that last...thinking out loud.

Your order of operations means that the content between parentheses comes before the *24.

(6x-6/8)24  = 24*(6x-6) / 24(8)

not

(6x-6/8)24  = (6x-6) / 24(8)
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Commented:
From 2nd to 3rd line:

24(4x/6) - 24(x+5/2) = (6x-6/8)24

24*4x/6 - 24x - 24*(5/2) = 144x - 144/8

Check why/if this is the case and continue there.

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Author Commented:
I appreciate your help, but I am just not understanding this. Here are the directions I am following.

To solve an equation with fractions

1. Find the least common denominator(LCD) of all fractional terms on both sides of the equation.
2. Multiply both sides of the equation by the LCD. (If this step has been done correctly, no fractions should now appear in the equation.)
3. Solve the resulting equation from step 2.
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Commented:
(6x-6/8)24    does not =    (6x-6)3

(6x-6/8)24 = 24(6x) - 24(6/8)  = 144x - 144/8  =  144x - 18

while

(6x-6)3 = 18x - 18
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Commented:
> The answer is x=-3. Where am I going wrong? Thanks.
>             4x/6 - x+5/2 = 6x-6/8

If you replace x with the claimed answer -3 in the first equation you'll get:

4 * (-3) / 6 - (-3) + 5/2 = 6 * (-3) - 6/8

or

-2 + 3 + 5/2 = -18 - 6/8

or in decimal form:

3.5 = -18.75

which obviously isn't correct. Are you sure you entered the initial equation correctly?

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Author Commented:
I entered the initial equation correctly.

When I plug -3 into the original equation to check it, it comes out -3 = -3.

4x/6 - x+5/2 = 6x-6/8

4(-3)/6 - -3+5/2 = 6(-3)-6/8

-12/6 - -3+5/2 = -18-6/8

-12/6 - 2/2 = -24/8

-3 = -24/8

-3 = -3
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Commented:
> -12/6 - -3+5/2 = -18-6/8
> -12/6 - 2/2 = -24/8

This step isn't correct, you need to apply the rules of orders of multiplication, division, addition and subscription.

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Author Commented:
Here is one of the examples out of the book. I won't finish it. 24 is the LCD. This reduces the fraction to just numbers.

2x+1/3 - x-6/4 = 2x+4/8 +2

24(2x+1/3 - x-6/4) = (2x+4/8 + 2)24

24(2x+1/3) - 24(x-6/4) = (2x+4/8)24 + 2(24)

8(2x+1) - 6(x-6) = 3(2x+4) + 48

16x + 8 - 6x + 36 = 6x +12 + 48

10x + 44 = 6x + 60
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Author Commented:
Maybe I should have written it

(-3+5)/2
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Commented:
Yes exactly. When you write the equations in horizontal text format, you should always use plenty of parenthesis to avoid confusion. As an example, if you want to write "sum of -3 + 5 divided by 2", you should write:

(-3 + 5) / 2

-3 + 5 / 2

... because us readers can not see the same layout you see in your text book and automatically assume "-3 + 5 / 2" means "sum of -3 and 2.5" instead of "sum of -3 and 5 divided by 2".

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Commented:
If in doubt, add parenthesis - it helps keep things organized and allows others to see what should be grouped, and what should not
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Author Commented:
In this similar equation, the first goal is to get rid of the fractions by finding the LCD of 3, 4 and 8 is 24. 3 goes into 24  8 times. 4 into 24  6 times and 8 into 24 3 times. Thus 8(2x+1) - 6(x-6) = 3(2x+4) + 48 the fraction is now gone. All of the examples in my book follow this pattern.

2x+1/3 - x-6/4 = 2x+4/8 +2

24(2x+1/3 - x-6/4) = (2x+4/8 + 2)24

24(2x+1/3) - 24(x-6/4) = (2x+4/8)24 + 2(24)

8(2x+1) - 6(x-6) = 3(2x+4) + 48

16x + 8 - 6x + 36 = 6x +12 + 48

10x + 44 = 6x + 60
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Commented:
Can you re-type the original problem Line 1 using proper parentheses?

I'm lost now as to what your original question is.

We all understand your method, and have pointed out errors in your order of operations, but I think it's because you're not transcribing the problem correctly into typewritten form.
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Author Commented:

4x/6 - x+5/2 = 6x-6/8

24(4x/6) - 24(x+5/2) = (6x-6/8)24

4(4x) - 12(x+5) = (6x-6)3

16x - 12x-60 = 18x-18

4x-60 = 18x-18
-4x          -4x

-60 = 12x-18
+18 =      +18

-42 = 12x

-42/12 = 12x/12

-7/2 = x
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Commented:
right side, from Line2 to Line3

(6x-6/8)24   does not =  (6x-6)3

Only if the Line1 is written ((6x-6)/8)*24.  But you wrote     6x - 6/8

So...are you missing some parentheses?
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Author Commented:
Thanks for your on going help. The book answer is -3 and it's true when I check the problem.

If I am missing parentheses then the book must also be wrong.
Here is example 5 from the book that shows how to solve the same kind of problem.
(2x+4/8)24 = 3(2x+4)

2x+1/3 - x-6/4 = 2x+4/8 +2

24(2x+1/3 - x-6/4) = (2x+4/8 + 2)24

24(2x+1/3) - 24(x-6/4) = (2x+4/8)24 + 2(24)

8(2x+1) - 6(x-6) = 3(2x+4) + 48

16x + 8 - 6x + 36 = 6x +12 + 48

10x + 44 = 6x + 60

Maybe I can post a photo of the book example and the problem I am having trouble with. If you think that will help I will gladly do so.
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Commented:
Giving other examples of different problems is just confusing things.  It's not the method.  It's your notation.

Answers and answer keys in the back of textbooks are not always right.  They have human beings writing those, and human beings checking them.  Sometimes mistakes get through.

That aside, do you see what I'm saying with this? -->  (6x-6/8)24   does not =  (6x-6)3
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Author Commented:
(6x-6/8)24

6x-6 24
8    1

8 goes into 8 once and goes into 24 3 times.

(6x-6)3

The 8 in the fraction is now gone.

None of the examples in the book add these extra parentheses and anyway why would you need this * to multiply when you already have parentheses which tell you to multiply.

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Commented:
(6x-6/8)24  =  (6x)24 - (6/8)24

>None of the examples in the book add these extra parentheses

Because you are staring at nicely formatted text in a book.  We're looking at your translation into a single line of typewritten text.

In your translation, you're not providing enough parentheses to keep the numerator "6x-6" as a single number.  You keep typing it as "6x-6/8", when it should be (I'm guessing) "(6x-6)/8"

>why would you need this * to multiply

It's implied when omitted.  I put it there for clarification.  Neither is right nor wrong.

I think I'll bow out now.  Clearly we are not speaking the same language, and I'm not helping.
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Author Commented:

I did not add parentheses to the other side of the equation either. Why was that not pointed out?

It would be nice if someone could just do the problem so it equals -3. I would think that would clear things up.
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Author Commented:
I wish I could award points for your effort.
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Commented:
I think I see why both of you are confused.
When you write 6x-6/8, you mean 6x/8 - 6/8 right?
algehart (and everyone else) would write that as (6x-6)/8 so that you know both are over the 8. We would read what you wrote as the 6x not being over the 8.
I'm posting two pictures. Tell us which is the correct equation.
The way you wrote it is the same as B. Look carefully and you'll see why. In your equation, how do you know what goes over what? I know it looks right to you, but we all see B when we see that.
I know you meant it to be A. You should write it like this then:
4x/6 - (x+5)/2 = (6x-6)/8
Then everyone will understand.

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Commented:
Your only problem is that you took 18x - 4x and got 12x. Should be 16x.
4x/6 - x+5/2 = 6x-6/8

24(4x/6) - 24(x+5/2) = (6x-6/8)24

4(4x) - 12(x+5) = (6x-6)3

16x - 12x-60 = 18x-18

4x-60 = 18x-18
-4x          -4x

-60 = 12x-18  -60=14x-81

+18 =      +18

-42/14 = 14x/14

-42/14 = x

Which of course gives you what you already knew.
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Author Commented:
Thank you.

It is amazing how much we can see and still be blind.
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