document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=958406>Question 958406</A>: <I><SPAN STYLE=\"word-break: break-all;\"> need help just cant figure out these problems , have to solve the equations<BR>\n" );
document.write( "|2x-7|=3<BR>\n" );
document.write( "|x-6|=|2x+1|<BR>\n" );
document.write( "|x-4|<3<BR>\n" );
document.write( "|x/3 - 1|&#8805;2\r<BR>\n" );
document.write( "\n" );
document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854588 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13367)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=854588\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The other tutors solve the problems by considering different cases; that is the standard formal algebraic method.<br><BR>\n" );
document.write( "For problems (a), (c), and (d) -- in which there is an absolute value expression on only one side -- the solutions can be found by a different method.<br><BR>\n" );
document.write( "The statement <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-a%29=b ALIGN=MIDDLE  ALT=\"abs%28x-a%29=b\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be interpreted to say \"the difference between (variable) x and (fixed) a is equal to b\".<br><BR>\n" );
document.write( "For (c), this can lead directly to the answer.  The equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-4%29=3 ALIGN=MIDDLE  ALT=\"abs%28x-4%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > says that the difference between x and 4 is equal to 3, which means the values of x are 4-3=1 and 4+3=7.  Then since the statement is in fact a strict \"less than\" inequality, 1 and 7 are the boundaries of the solution set, so the solution in interval notation is (1,7).<br><BR>\n" );
document.write( "For (a) and (d) we need to multiply the whole inequalities by appropriate constants to make \"x\" appear by itself in the absolute value expression.<br><BR>\n" );
document.write( "(a)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%282x-7%29=3 ALIGN=MIDDLE  ALT=\"abs%282x-7%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-3.5%29=1.5 ALIGN=MIDDLE  ALT=\"abs%28x-3.5%29=1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The solutions are the two numbers for which the difference between the number and 3.5 is 1.5 -- i.e., 3.5-1.5 = 2 and 3.5+1.5 = 5.<br><BR>\n" );
document.write( "(d)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x%2F3-1%29%3E=2 ALIGN=MIDDLE  ALT=\"abs%28x%2F3-1%29%3E=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-3%29%3E=6 ALIGN=MIDDLE  ALT=\"abs%28x-3%29%3E=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The boundaries of the solution set are the two numbers whose difference from 3 is 6 -- i.e., 3-6 = -3 and 3+6 = 9.  Then since the statement is an inclusive \"greater than\" inequality, the solution set in interval notation is (-infinity,-3] U [9,infinity).<br><BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );