document.write( "Question 1119204: I kind of get that when you are solving an inequality like ∣5x+1∣>3 that you are supposed to do it in two cases. But, what I don't get is why one of those cases is 5x+1<−3 because I thought that absolute values can never be negative. Why do we do that case? \n" ); document.write( "

Algebra.Com's Answer #734692 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "1.  If you are given inequality  |a| > 3 for real number \"a\", it means that\r\n" );
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document.write( "    EITHER  a > 3  OR  a < -3.\r\n" );
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document.write( "    It is VERY FIRST thing you need to understand.\r\n" );
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document.write( "    The rest is just technique, which I'll show you below.\r\n" );
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document.write( "    To get this understanding, use the visual image of the number line and remember that |a| > 3 means that the distance from \"a\" to 0\r\n" );
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document.write( "    (to zero) is greater than 3.\r\n" );
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document.write( "2.  After you got this understanding, the rest is MUCH EASIER.\r\n" );
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document.write( "    So,  |5x+1| > 3 means that \r\n" );
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document.write( "    EITHER  5x+1 > 3   OR  5x+1 < -3.\r\n" );
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document.write( "3.  Let us consider the case  \r\n" );
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document.write( "    5x+1 > 3     (1)\r\n" );
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document.write( "    first.  Subtract 1 from both sides. You will get\r\n" );
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document.write( "    5x > 3 - 1 = 2.    Divide by 5 both sides. You will get\r\n" );
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document.write( "    x > ,   or   x > 0.4.\r\n" );
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document.write( "    It is your solution for the case (1).\r\n" );
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document.write( "4.  Next consider the case\r\n" );
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document.write( "    5x + 1 < -3.\r\n" );
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document.write( "    Subtract 1 from both sides. You will get\r\n" );
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document.write( "    5x < -3 -1 = -4.\r\n" );
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document.write( "    Divide by 5 both sides. You will get\r\n" );
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document.write( "    x <   or  x < -0.8.\r\n" );
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document.write( "    It is your solution for the case (2).\r\n" );
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document.write( "5.  Thus the set of solutions to the given inequality is the UNION of two semi-infinite intervals\r\n" );
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document.write( "    { x < -4/5 }   U   { x > 2/5 }.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "If after my explanations you still have questions, do not hesitate post them to the forum.\r
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\n" ); document.write( "\n" ); document.write( "I wrote my solution, because the solution by the other tutor contained some errors on the way, that could confuse you.\r
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\n" ); document.write( "\n" ); document.write( "So, I rectified his solution and his answer as well.\r
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