document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127367>Question 127367</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can you please help me solve this problem step by step. This is linear inequalities probelm 5(x+1)<3x+4 =\r<BR>\n" );
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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 #93326 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=93326\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28x%2B1%29%3C3x%2B4 ALIGN=MIDDLE  ALT=\"5%28x%2B1%29%3C3x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve inequalities the same way you solve equations, with two important exceptions.  First, if you multiply or divide both sides of the inequality by a negative number, you must reverse the sense of the inequality.\r<BR>\n" );
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document.write( "For example, we know it is true that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%3C1 ALIGN=MIDDLE  ALT=\"-2%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but if we multiply both sides of the inequality by -1, we get 2 on the left and -1 on the right.  The 'less than' symbol is no longer correct, it must be changed to 'greater than' because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%3E-1 ALIGN=MIDDLE  ALT=\"2%3E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The second exception is that the solution set will be represented by an interval rather than a single value.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28x%2B1%29%3C3x%2B4 ALIGN=MIDDLE  ALT=\"5%28x%2B1%29%3C3x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Distribute and remove parentheses<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B5%3C3x%2B4 ALIGN=MIDDLE  ALT=\"5x%2B5%3C3x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add -3x to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-3x%2B5%3C4 ALIGN=MIDDLE  ALT=\"5x-3x%2B5%3C4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B5%3C4 ALIGN=MIDDLE  ALT=\"2x%2B5%3C4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add -5 to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%3C4-5 ALIGN=MIDDLE  ALT=\"2x%3C4-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%3C-1 ALIGN=MIDDLE  ALT=\"2x%3C-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Finally, divide both sides by 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C-1%2F2 ALIGN=MIDDLE  ALT=\"x%3C-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the solution set is {x| x is real, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C-1%2F2 ALIGN=MIDDLE  ALT=\"x%3C-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >}.  You can also use interval notation (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >).   Note the parentheses around the interval.  Had the problem included the possiblity of equality, i.e. had it been <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28x%2B1%29%3C=3x%2B4 ALIGN=MIDDLE  ALT=\"5%28x%2B1%29%3C=3x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the interval would have been denoted by <BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >].   \r<BR>\n" );
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document.write( "Since we never multiplied or divided by a number that is <0, the sense of the inequality remains as it was in the original inequality. </SPAN>\n" );
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