document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170680>Question 1170680</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The results of a poll claiming a 4% margin of error indicated that a candidate was favored by 48% of the voters. Write an absolute value inequality representing the percent of voters favoring the candidate. Then solve the inequality to state the range of the candidate's support.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851118 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851118\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down this problem step by step.\r<BR>\n" );
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document.write( "**1. Define the Variable**\r<BR>\n" );
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document.write( "Let 'x' represent the actual percentage of voters favoring the candidate.\r<BR>\n" );
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document.write( "**2. Write the Absolute Value Inequality**\r<BR>\n" );
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document.write( "The margin of error (4%) means the actual percentage could be 4% higher or 4% lower than the poll result (48%). This can be represented as:\r<BR>\n" );
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document.write( "|x - 48| ≤ 4\r<BR>\n" );
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document.write( "**3. Solve the Absolute Value Inequality**\r<BR>\n" );
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document.write( "To solve the absolute value inequality, we need to consider two cases:\r<BR>\n" );
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document.write( "* **Case 1:** x - 48 ≤ 4<BR>\n" );
document.write( "   * Add 48 to both sides:<BR>\n" );
document.write( "     * x ≤ 52\r<BR>\n" );
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document.write( "* **Case 2:** -(x - 48) ≤ 4<BR>\n" );
document.write( "   * Multiply both sides by -1 (and reverse the inequality sign):<BR>\n" );
document.write( "     * x - 48 ≥ -4<BR>\n" );
document.write( "   * Add 48 to both sides:<BR>\n" );
document.write( "     * x ≥ 44\r<BR>\n" );
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document.write( "**4. State the Range of Candidate's Support**\r<BR>\n" );
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document.write( "Combining the two cases, we get:\r<BR>\n" );
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document.write( "44 ≤ x ≤ 52\r<BR>\n" );
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document.write( "**Therefore:**\r<BR>\n" );
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document.write( "* **Absolute Value Inequality:** |x - 48| ≤ 4<BR>\n" );
document.write( "* **Range of Candidate's Support:** The candidate is favored by between 44% and 52% of the voters.<BR>\n" );
document.write( " </SPAN>\n" );
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