document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=100887>Question 100887</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm taking a elementary and intermediate algebra in college. It's been a very long while since I have done algebra. I'm trying to figure out where do I start first within this expression\r<BR>\n" );
document.write( "\n" );
document.write( "[3-(2-4)][3+|2-4|]\r<BR>\n" );
document.write( "\n" );
document.write( "also \r<BR>\n" );
document.write( "\n" );
document.write( "8-3|5-4 2ndpower + 1| </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #73516 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=73516\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First problem. Given:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "[3-(2-4)][3+|2-4|]<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We can start by working this in two parts. [3-(2-4)] is one part and [3+|2-4|] is the other.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "For the part [3-(2-4)] start with the \"nested\" or interior set of parentheses. In those<BR>\n" );
document.write( "parentheses you have (2-4) and when you combine those two numbers, the result is (-2). Therefore,<BR>\n" );
document.write( "you can substitute (-2) with its parentheses and you get [3-(-2)]. Since the parentheses<BR>\n" );
document.write( "are preceded by a minus sign you can remove them if you change the sign of the number inside<BR>\n" );
document.write( "the parentheses. (You can also look at this as a multiplication of the number inside the<BR>\n" );
document.write( "parentheses by a minus 1.) When you remove the parentheses you get [3 + 2] and this simplifies<BR>\n" );
document.write( "to [5]. So the first part is just [5] <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Next work the second part which is [3+|2-4|]. I assume that the \"|\" and \"|\" enclosures are<BR>\n" );
document.write( "the standard notation meaning absolute value. The absolute value symbols mean that anything<BR>\n" );
document.write( "inside them will come outside as a positive value.  So let's start with the \"nested\" or <BR>\n" );
document.write( "interior set of absolute value signs which are |2-4|. Combine the two interior numbers and<BR>\n" );
document.write( "you get |-2|. But the absolute value of |-2| = (+2) by the definition of absolute value. Making<BR>\n" );
document.write( "this substitution in two steps you get [3+ (+2)] and since the parentheses are preceded by<BR>\n" );
document.write( "a plus sign, they can be removed without changing the sign of their contents to get just<BR>\n" );
document.write( "[3 + 2]. Simplify this by just adding the two numbers to get [5]. This means that <BR>\n" );
document.write( "[3+|2-4|] is equal to [5].<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So now we have reduced the two parts of the original problem and we substitute the equivalent<BR>\n" );
document.write( "values for [3-(2-4)][3+|2-4|] to get [5][5] and this multiplication results in the answer<BR>\n" );
document.write( "for this problem being 25.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Onward to the second problem: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8-3%2Aabs%285-4%5E2+%2B+1%29 ALIGN=MIDDLE  ALT=\"8-3%2Aabs%285-4%5E2+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "I hope that I interpreted correctly what you wrote. Start inside the absolute value signs.<BR>\n" );
document.write( "First, let's square the 4 to get 16. [Notice that you interpret this as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%284%5E2%29=+-16 ALIGN=MIDDLE  ALT=\"-%284%5E2%29=+-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and not as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%29%5E2=+16 ALIGN=MIDDLE  ALT=\"%28-4%29%5E2=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.] When you substitute this into the problem you have:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8-3%2Aabs%285-16%2B1%29 ALIGN=MIDDLE  ALT=\"8-3%2Aabs%285-16%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now combine the three numbers inside the absolute value signs. 5-16+1 combine to -10. Substitute<BR>\n" );
document.write( "this into the problem and you have:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+-3%2Aabs%28-10%29 ALIGN=MIDDLE  ALT=\"8+-3%2Aabs%28-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "but recall the definition of absolute value. The absolute value of -10 is +10, so you can <BR>\n" );
document.write( "replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28-10%29 ALIGN=MIDDLE  ALT=\"abs%28-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%29 ALIGN=MIDDLE  ALT=\"%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the problem becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+-3%2A%2810%29 ALIGN=MIDDLE  ALT=\"8+-3%2A%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now you do the multiplication of -3 times 10 to get -30 and with that substitution <BR>\n" );
document.write( "the problem becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+-+30 ALIGN=MIDDLE  ALT=\"8+-+30\"   DISABLED_style= \"max-width:90%; height:auto;\" > and these two numbers combine to give <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-22 ALIGN=MIDDLE  ALT=\"-22\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the answer<BR>\n" );
document.write( "to this problem is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-22 ALIGN=MIDDLE  ALT=\"-22\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "As a final note, the general order of algebraic manipulations is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "1. Do things in parentheses or other grouping symbols first, working from the interior sets outward<BR>\n" );
document.write( "2. Do the exponential terms<BR>\n" );
document.write( "3. From left to right do the multiplications and divisions as you encounter them.<BR>\n" );
document.write( "4. From left to right do the additions and subtractions as you encounter them<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Takes a lot of practice before you get the hang of doing these things ... so hang tough.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope I correctly interpreted the way you wrote these two problems and I hope this helps you<BR>\n" );
document.write( "to understand the concept of working your way from the inside set of parentheses or \"groupings\"<BR>\n" );
document.write( "to the outside set.<BR>\n" );
document.write( ". </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );