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
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.
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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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
instead of:
-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".
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.
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.
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.
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
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.
>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.
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.
It is amazing how much we can see and still be blind.
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