document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=270154>Question 270154</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this step by step:\r<BR>\n" );
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document.write( "5|5x-7|is greater than or equal to 110\r<BR>\n" );
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document.write( "I have to graph it and put into interval also.\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 #197970 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=197970\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your equation is:\r<BR>\n" );
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document.write( "5*|5x-7| >= 110\r<BR>\n" );
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document.write( "If the expression within the absolute value sign is positive, then the expression becomes:\r<BR>\n" );
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document.write( "5*(5x-7) >= 110\r<BR>\n" );
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document.write( "Simplify this equation to get:\r<BR>\n" );
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document.write( "25x - 35 >= 110\r<BR>\n" );
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document.write( "Add 35 to both sides of this equation to bet:\r<BR>\n" );
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document.write( "25x >= 110+35 = 145\r<BR>\n" );
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document.write( "Divide both sides of this equation by 25 to get:\r<BR>\n" );
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document.write( "x >= 145/25 = 5.8\r<BR>\n" );
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document.write( "If the expression within the absolute value sign is negative, then the equation becomes\r<BR>\n" );
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document.write( "5 * (-(5x-7)) >= 110\r<BR>\n" );
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document.write( "Simplify this equation to get:\r<BR>\n" );
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document.write( "5 * (-5x + 7) >= 110\r<BR>\n" );
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document.write( "Simplify further to get:\r<BR>\n" );
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document.write( "-25*x + 35 >= 110\r<BR>\n" );
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document.write( "Subtract 35 from both sides of this equation to get:\r<BR>\n" );
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document.write( "-25*x >= 110-35 = 75\r<BR>\n" );
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document.write( "Divide both sides of this equation by -25 to get:\r<BR>\n" );
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document.write( "x <= 75/-25 = -3\r<BR>\n" );
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document.write( "The answer to your question should be\r<BR>\n" );
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document.write( "x >= 5.8 or x <= -3\r<BR>\n" );
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document.write( "You have to confirm these answers are good by testing with values inside the limits and outside the limits.\r<BR>\n" );
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document.write( "When x = 5.8, 5 * |5x-7| >= 110 becomes 5 * |29-7| = 5*22 = 110 which is true because the equation says >= and this is =.\r<BR>\n" );
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document.write( "When x = -3, 5* |5x-7| >= 110 becomes 5 * |-15-7| = 5*|-22| = 5*22 = 110 which is also true because the equation says >= and this is =.\r<BR>\n" );
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document.write( "When x = 0, 5*|5x-7| >= 110 becomes 5*|-7| = 5*7 = 35 which is NOT true because 35 is not greater than or equal to 110.\r<BR>\n" );
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document.write( "Since when x = 0, it is NOT greater than 5.8 and it is NOT less than -3, this is good because the equation should NOT have been satisfied when x = 0.\r<BR>\n" );
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document.write( "When x = -5, 5 * |5x-7| >= 110 becomes 5 * |-25-7| becomes 5 * |-32| becomes 5 * 32 = 160 >= 110 which is true.\r<BR>\n" );
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document.write( "When x = 7, 5 * |5x-7| >= 110 becomes 5 * |35-7| becomes 5 * |28| becomes 5 * 28 = 140 >= 110 which is true.\r<BR>\n" );
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document.write( "The answer looks good.\r<BR>\n" );
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document.write( "When we are within the stated limits of x, our equation becomes true.\r<BR>\n" );
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document.write( "When we are outside the stated limits of x, our equation becomes false.\r<BR>\n" );
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document.write( "Your answer is:\r<BR>\n" );
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document.write( "x >= 5.8 or x <= -3\r<BR>\n" );
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document.write( "In terms of intervals this would appear as (-infinity,-3] union [5.8,infinity}\r<BR>\n" );
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document.write( "A graph of your equation would look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-10%2C200%2C5%2Aabs%285x-7%29%2C110%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-10%2C200%2C5%2Aabs%285x-7%29%2C110%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you draw a vertical line at x = -3 and a vertical line at x = 5.8, you will see that the value of y is greater than or equal to 110 to the left of the x = -3 vertical line and to the right of the x = 5.8 vertical line.\r<BR>\n" );
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document.write( "All of this stems from the basic definition of absolute value that states:\r<BR>\n" );
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document.write( "absolute value of x = x if x is positive, and equals -x if x is negative.\r<BR>\n" );
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document.write( "The \"x\" in this case is the expression (5x-7) that is within the absolute value sign.\r<BR>\n" );
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document.write( "the absolute value of 5x-7 equals 5x-7 if the expression 5x-7 is positive.\r<BR>\n" );
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document.write( "the absolute value of 5x-7 equals -(5x-7) if the expression 5x-7 is negative.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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