Expert: Josh - 2/4/2009

Question
I am stuck on a math problem that involves adding coefficients. I will type in the part that I just do not understand:      > x + 2 = 0.50x + 2.5
           > -0.50x      -0.50x
             > 0.5x = 2 = 2.5
The arrows indicate where I lose my understanding of coefficients. I thought the way to solve it was to subtract 0.50x from x which would equal -0.49x, but apparently that is not the case. Please help shed some knowledge to me. :) Thanks.  

Answer
Response to comments from questioner.

Note 1: I accept the questioner's criticism that the response may not be clear. To be fair, it is not possible for me to know what the questioner is or is not familiar with, since he/she did not mention his/her background. Regarding the use of acronyms, LHS and RHS (Left Hand Side and Right Hand Side) are pretty standard terms. The questioner could easily have asked a follow-up to clarify the meaning of any words or look up those terms on a web search engine.

Note 2: Regarding politeness, I would rather let others be the judge. What have I to gain from being sarcastic to someone I do not even know? That is not the person I am. Sorry you feel that way. Would you not agree that it would be courteous to address the volunteer in name before opening the question.

Note 3: Re: "the volunteerer[sic] made a commit[sic] that I am confused. I am not confused, just can't remember what I was taught 30 years ago regarding coefficients". Let's look at the evidence objectively. You may not have realized, but the mathematical expressions you presented contain a number of inconsistencies which made those statements ambiguous and difficult to follow. Whilst the internet scripting language may have altered your original syntax, I can only judge from the logical content that I see before me which indicates some level of confusion. With due respect, I have to be brutally honest and point out those mistakes so that you may come to a better understanding of what went wrong. This, I did, in the sixth paragraph. I am not sure whether "subtract 0.50x from x which would equal -0.49x" may have originated from a typgraphical error.

Note 4: I meant no sarcasm when I said "I'm glad that you asked this question." It is commendable that you are taking positive action trying to remove doubts which may hold you back in your learning. That's all to it.
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>>>Original Reply:

Hello M

I actually would have preferred seeing the original expression, since it would be easier to spot where potential mistakes are made.

The bottom line is this: whatever amount you add (or subtract), multiply (or divide) you do the same to both sides of the equation; that way you cannot go wrong -- unless you make arithmetic mistakes.

If we begin with x+2=0.5x+2.5, as you rightly pointed out, our goal is to keep the unknown ("x") on one side of the equation. We do this by subtracting 0.5x from both sides.

The LHS x+2-0.5x becomes 0.5x+2. (Note: subtracting half x from one x leaves us with half x, not -0.49x as you claimed.)
The RHS 0.5x+2.5-0.5x becomes 2.5. So we now have 0.5x+2=2.5.

The next step is to subtract 2 from both sides. This leaves us with 0.5x = 0.5. You can divide both sides by 0.5 to get x=1 as the final answer.

Referring to your query, the part where you said "> -0.50x -0.50x" does not follow from the previous line. The next part "> 0.5x = 2 = 2.5" also makes no sense (the assertion that 2 equals 2.5 is obviously not true). So I'm not surprised that you find it confusing.
            
The steps you should take are summarized below:

x+2=0.5x+2.5  [Step 1: subtract 0.5x from both sides to isolate the "x" keeping it on one side of the equation]
0.5x+2=2.5    [Step 2: subtract 2 from both sides of the equation to keep the known values (the constants or numbers) on the opposite side of the unknown (x variable)]
0.5x=0.5 [Step 3: divide both sides by 0.5, OR multiply both sides by 2 to arrive at the final solution]
x=1

I'm glad that you asked this question.