document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1078028>Question 1078028</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rewrite without using absolute value sign: <BR>\n" );
document.write( "|x-2|<4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #692496 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=692496\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the basic definition of absolute value is:\r<BR>\n" );
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document.write( "abs(x) = x if x is positive and equals -x if x is negative.\r<BR>\n" );
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document.write( "x represents any expression that is included as an argument in the absolute value function.\r<BR>\n" );
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document.write( "therefore:\r<BR>\n" );
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document.write( "abs(x-2) < 4 becomes:\r<BR>\n" );
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document.write( "(x-2) < 4 if (x-2) is positive, .....\r<BR>\n" );
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document.write( "and -(x-2) < 4 if (x-2) is negative.\r<BR>\n" );
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document.write( "when (x-2) is positive, you would solve for x as follows:\r<BR>\n" );
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document.write( "x-2 < 4<BR>\n" );
document.write( "add 2 to both sides of the inequality to get:<BR>\n" );
document.write( "x < 6\r<BR>\n" );
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document.write( "when (x-2) is negative, you would solve for x as follows:\r<BR>\n" );
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document.write( "-(x-2) < 4<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "-x + 2 < 4<BR>\n" );
document.write( "subtract 2 from both sides to get:<BR>\n" );
document.write( "-x < 2<BR>\n" );
document.write( "multiply both sides by -1 to get:<BR>\n" );
document.write( "x > -2\r<BR>\n" );
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document.write( "don't forget that multiplying both sides of an inequality by the same negative number reverses the inequality.\r<BR>\n" );
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document.write( "so your answer is:\r<BR>\n" );
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document.write( "x < 6 or x > -2\r<BR>\n" );
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document.write( "this can be written as -2 < x < 6\r<BR>\n" );
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document.write( "abs(x-2) < 4 when x is greater than 2 and when x is < 6\r<BR>\n" );
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document.write( "to test this out, let x equal values that satisfy the solution and that do not satisfy that solution.\r<BR>\n" );
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document.write( "any value of x > -2 and < 6 will satisfy the solution.\r<BR>\n" );
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document.write( "i choose 4\r<BR>\n" );
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document.write( "when x = 4, abs(x-2) < 4 becomes abs(4-2) < 4 which becomes abs(2) < 4 which becomes 2 < 4 which is true.\r<BR>\n" );
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document.write( "i choose x = -3 and x = 7 as values which do not satisfy the solution range.\r<BR>\n" );
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document.write( "when x = -3, abs(x-2) < 4 becomes abs(-3-2) < 4 which becomes abs(-5) < 4 which becomes 5 < 4 which is false.\r<BR>\n" );
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document.write( "when x = 7, abs(x-2) < 4 becomes abs(7-2) < 4 which becomes abs(5) < 4 which becomes 5 < 4 which is false.\r<BR>\n" );
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document.write( "you can also graph the equation of y = abs(x) and y = 4 and it will show you graphically when the equation of y = abs(x) is smaller than 4.\r<BR>\n" );
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document.write( "that graph is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/042402.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "from the graph, you can see that the value of y = abs(x-2) is less than the value of y = 4 when x is greater than -2 through x is smaller than 6 only.\r<BR>\n" );
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document.write( "the coordinate points are shown in the format of (x,y), where x represents the value of the x-coordinate and y represents the value of the y coordinate.\r<BR>\n" );
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document.write( "for example, when x = -2, then the value of y = abs(x-2) becomes y = abs(-2-2) which becomes y = abs(-4) which becomes y = 4, which provides you with the coordinate point of (-2,4).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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