document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116847>Question 116847</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84963 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=84963\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If it's any consolation, I don't agree with the \"recipe\" method of solving problems, <BR>\n" );
document.write( "meaning that \"this is the only order\" you can solve this problem. It really is more important<BR>\n" );
document.write( "that whatever order you use, it is more important to you to understand what you did and<BR>\n" );
document.write( "why you did it. Just look at your case. You worked the problem and apparently did it correctly.<BR>\n" );
document.write( "Now you are being confused by a teacher that says ... you must do it exactly this way or else<BR>\n" );
document.write( "you get no credit. Adding confusion is counterproductive to education.<BR>\n" );
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document.write( "That being said, here's what the teacher wanted you to do:<BR>\n" );
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document.write( "Step 1. Simplify each side separately. Just work on one side at a time with the goal of <BR>\n" );
document.write( "combining terms as much as you can. Start with the left side which is:<BR>\n" );
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document.write( "0.8 - 4(X-1) <BR>\n" );
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document.write( "Do the distributed multiplication by multiplying -4 times each of the terms inside the<BR>\n" );
document.write( "parentheses and you get:<BR>\n" );
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document.write( "0.8 - 4X + 4<BR>\n" );
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document.write( "Now combine the 0.8 and the +4 to get 4.8<BR>\n" );
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document.write( "This reduces the left side to:<BR>\n" );
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document.write( "-4X + 4.8<BR>\n" );
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document.write( "So we can replace the left side in the original equation with -4X + 4.8 and the problem becomes:<BR>\n" );
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document.write( "-4X + 4.8 = 0.2 + 3(4-X) <=== Remember this<BR>\n" );
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document.write( "Now let's do the same type process on the right side of the equation only. Do the distributed<BR>\n" );
document.write( "multiplication by multiplying +3 times each of the terms inside the parentheses. So start with<BR>\n" );
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document.write( "0.2 + 3(4 - X) <BR>\n" );
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document.write( "and after the distributed multiplication you have:<BR>\n" );
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document.write( "0.2 + 12 - 3X<BR>\n" );
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document.write( "Combine the 0.2 and the +12 to get 12.2 and substitute this result to make the entire right<BR>\n" );
document.write( "side:<BR>\n" );
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document.write( "12.2 - 3X<BR>\n" );
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document.write( "Put this new right side into the \"remember this\" equation above to make it:<BR>\n" );
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document.write( "-4X + 4.8 = 12.2 - 3X<BR>\n" );
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document.write( "That completes Step 1. We simplified each side by itself.<BR>\n" );
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document.write( "Step 2. Isolate the variable term on one side. <BR>\n" );
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document.write( "In the equation that we ended up with in Step 1 we need to get all the terms that contain<BR>\n" );
document.write( "X on one side and all the numbers on the other side. Start with:<BR>\n" );
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document.write( "-4X + 4.8 = 12.2 - 3X<BR>\n" );
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document.write( "Get rid of the -3X on the right side by adding +3X to both sides to get:<BR>\n" );
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document.write( "-4X + 3X + 4.8 = 12.2 - 3X + 3X<BR>\n" );
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document.write( "On the right side the -3X and +3X cancel each other out and are gone. So the equation that<BR>\n" );
document.write( "remains is:<BR>\n" );
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document.write( "-4X + 3X + 4.8 = 12.2<BR>\n" );
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document.write( "Get rid of the +4.8 on the left side by subtracting 4.8 from both sides to get:<BR>\n" );
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document.write( "-4X + 3X + 4.8 - 4.8 = 12.2 - 4.8<BR>\n" );
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document.write( "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<BR>\n" );
document.write( "combine to give 7.4. So the resulting equation is:<BR>\n" );
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document.write( "-4X + 3X = 12.2 - 4.8<BR>\n" );
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document.write( "That completes Step 2, isolate the variable term on one side. The variable is now on the<BR>\n" );
document.write( "left side.<BR>\n" );
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document.write( "Step 3 Isolate the variable (x= a number) Begin with:<BR>\n" );
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document.write( "-4X + 3X = 12.2 - 4.8<BR>\n" );
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document.write( "Combine the two terms on the left side. -4X and + 3X combine to get -X. On the right side<BR>\n" );
document.write( "combine 12.2 and -4.8 to get 7.4. These two processes leave you with:<BR>\n" );
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document.write( "-X = 7.4<BR>\n" );
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document.write( "You are trying to solve for +X. So to make the left side be +X, multiply both sides by<BR>\n" );
document.write( "-1 and the equation becomes:<BR>\n" );
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document.write( "X = -7.4<BR>\n" );
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document.write( "That completes Step 3.<BR>\n" );
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document.write( "Step 4 Check. Substitute the proposed solution .<BR>\n" );
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document.write( "This means return to the given problem, substitute -7.4 for X, and see if one side of the<BR>\n" );
document.write( "resulting equation equals the other side, just as it should.<BR>\n" );
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document.write( "The original equation is:<BR>\n" );
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document.write( "0.8 - 4(X-1) = 0.2 + 3(4-X)<BR>\n" );
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document.write( "Put -7.4 into this equation wherever you see an X. When you do that you get:<BR>\n" );
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document.write( "0.8 - 4(-7.4 - 1) = 0.2 + 3(4 - (-7.4))<BR>\n" );
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document.write( "Do the multiplication. On the left side multiply -4 by the two terms in the parentheses to get:<BR>\n" );
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document.write( "0.8 + 29.6 + 4 = 0.2 + 3(4 - (-7.4))<BR>\n" );
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document.write( "On the right side the multiplication of +3 times the terms in the parentheses results in<BR>\n" );
document.write( "the right side as shown here:<BR>\n" );
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document.write( "0.8 + 29.6 + 4 = 0.2 + 12 + 22.2<BR>\n" );
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document.write( "Add up the numbers on both sides to get:<BR>\n" );
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document.write( "34.4 = 34.4<BR>\n" );
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document.write( "This shows that when X equals -7.4 both sides of the equation are equal and therefore,<BR>\n" );
document.write( "the answer we got checks.<BR>\n" );
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document.write( "That's my take on what the teacher was expecting to see in the answer to the problem.<BR>\n" );
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document.write( "Hope this helps.<BR>\n" );
document.write( ". </SPAN>\n" );
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