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Question 116847: 0.8 - 4(X-1) = 0.2 + 3(4-X), I had this one solved the other day and it was correct, but I was told that I did not have it in the right steps according to my project directions. Step 1-“Simplify each side separately. step2-Isolate the variable term on one side,step 3“Isolate the variable (x= a number)and step 4-“Check. Substitute the proposed solution . Can someone please explain this to me ? I don't understand how to show the problem step by step like that.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! If it's any consolation, I don't agree with the "recipe" method of solving problems,
meaning that "this is the only order" you can solve this problem. It really is more important
that whatever order you use, it is more important to you to understand what you did and
why you did it. Just look at your case. You worked the problem and apparently did it correctly.
Now you are being confused by a teacher that says ... you must do it exactly this way or else
you get no credit. Adding confusion is counterproductive to education.
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That being said, here's what the teacher wanted you to do:
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Step 1. Simplify each side separately. Just work on one side at a time with the goal of
combining terms as much as you can. Start with the left side which is:
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0.8 - 4(X-1)
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Do the distributed multiplication by multiplying -4 times each of the terms inside the
parentheses and you get:
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0.8 - 4X + 4
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Now combine the 0.8 and the +4 to get 4.8
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This reduces the left side to:
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-4X + 4.8
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So we can replace the left side in the original equation with -4X + 4.8 and the problem becomes:
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-4X + 4.8 = 0.2 + 3(4-X) <=== Remember this
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Now let's do the same type process on the right side of the equation only. Do the distributed
multiplication by multiplying +3 times each of the terms inside the parentheses. So start with
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0.2 + 3(4 - X)
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and after the distributed multiplication you have:
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0.2 + 12 - 3X
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Combine the 0.2 and the +12 to get 12.2 and substitute this result to make the entire right
side:
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12.2 - 3X
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Put this new right side into the "remember this" equation above to make it:
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-4X + 4.8 = 12.2 - 3X
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That completes Step 1. We simplified each side by itself.
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Step 2. Isolate the variable term on one side.
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In the equation that we ended up with in Step 1 we need to get all the terms that contain
X on one side and all the numbers on the other side. Start with:
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-4X + 4.8 = 12.2 - 3X
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Get rid of the -3X on the right side by adding +3X to both sides to get:
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-4X + 3X + 4.8 = 12.2 - 3X + 3X
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On the right side the -3X and +3X cancel each other out and are gone. So the equation that
remains is:
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-4X + 3X + 4.8 = 12.2
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Get rid of the +4.8 on the left side by subtracting 4.8 from both sides to get:
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-4X + 3X + 4.8 - 4.8 = 12.2 - 4.8
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On the left side the -4.8 and +4.8 combine to cancel out and on the right side the 12.2 and -4.8
combine to give 7.4. So the resulting equation is:
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-4X + 3X = 12.2 - 4.8
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That completes Step 2, isolate the variable term on one side. The variable is now on the
left side.
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Step 3 Isolate the variable (x= a number) Begin with:
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-4X + 3X = 12.2 - 4.8
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Combine the two terms on the left side. -4X and + 3X combine to get -X. On the right side
combine 12.2 and -4.8 to get 7.4. These two processes leave you with:
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-X = 7.4
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You are trying to solve for +X. So to make the left side be +X, multiply both sides by
-1 and the equation becomes:
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X = -7.4
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That completes Step 3.
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Step 4 Check. Substitute the proposed solution .
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This means return to the given problem, substitute -7.4 for X, and see if one side of the
resulting equation equals the other side, just as it should.
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The original equation is:
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0.8 - 4(X-1) = 0.2 + 3(4-X)
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Put -7.4 into this equation wherever you see an X. When you do that you get:
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0.8 - 4(-7.4 - 1) = 0.2 + 3(4 - (-7.4))
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Do the multiplication. On the left side multiply -4 by the two terms in the parentheses to get:
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0.8 + 29.6 + 4 = 0.2 + 3(4 - (-7.4))
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On the right side the multiplication of +3 times the terms in the parentheses results in
the right side as shown here:
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0.8 + 29.6 + 4 = 0.2 + 12 + 22.2
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Add up the numbers on both sides to get:
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34.4 = 34.4
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This shows that when X equals -7.4 both sides of the equation are equal and therefore,
the answer we got checks.
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That's my take on what the teacher was expecting to see in the answer to the problem.
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Hope this helps.
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