document.write( "Question 87518: This is giving me troubles please help me. Solve $\"abs%28%282x-1%29%2F5%29\"$ > $\"5%2F6\"$ \n" ); document.write( "

Algebra.Com's Answer #63444 by Edwin McCravy(20056) $\"\"$ $\"About$

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This is giving me troubles please help me. Solve $\"abs%28%282x-1%29%2F5%29\"$ > $\"5%2F6\"$ \r
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document.write( "Rules for getting rid of absolute value symbols in inequalities,\r\n" );
document.write( "The word \"EXPRESSION\" refers to whatever expression is between the\r\n" );
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document.write( "1.  |EXPRESSION| < A is equivalent to: -A < EXPRESSION < A\r\n" );
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document.write( "2.  |EXPRESSION| < A ie equivalent to: -A < EXPRESSION < A\r\n" );
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document.write( "3.  |EXPRESSION| > A ie equivalent to: EXPRESSION < -A OR EXPRESSION > A\r\n" );
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document.write( "04.  |EXPRESSION| > A ie equivalent to: EXPRESSION < -A OR EXPRESSION > A\r\n" );
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document.write( " > \r\n" );
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document.write( "This is case 4 with EXPRESSION =  and A = \r\n" );
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document.write( "Thus it is equivalent to:\r\n" );
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document.write( " <  OR  > \r\n" );
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document.write( "Multiply both sides of both inequalities by 30 to clear of fractions:\r\n" );
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document.write( " <  OR  > \r\n" );
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document.write( "6(2x - 1) < -25  OR  6(2x - 1) > 25\r\n" );
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document.write( "  12x - 6 < -25  OR  12x - 6 > 25\r\n" );
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document.write( "      12x < -19  OR  12x > 31\r\n" );
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document.write( "       x <   OR  x >      \r\n" );
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document.write( "Make three number lines:\r\n" );
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document.write( "Draw three number lines with a closed circle \r\n" );
document.write( "at the boundary points (closed because it's \r\n" );
document.write( "\"<\" OR \">\" and not \"<\" OR \">\"):\r\n" );
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document.write( "x <                  \r\n" );
document.write( "-----------l-------------l----------\r\n" );
document.write( "                          \r\n" );
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document.write( "x >                     \r\n" );
document.write( "-----------l-------------l----------\r\n" );
document.write( "                     \r\n" );
document.write( "                                                                            \r\n" );
document.write( "x < OR x >   \r\n" );
document.write( "-----------l-------------l----------\r\n" );
document.write( "                    \r\n" );
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document.write( "Shade the first one to the left of , because\r\n" );
document.write( "\"less than\" is \"left\":\r\n" );
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document.write( "x <\r\n" );
document.write( "<==========l-------------l----------\r\n" );
document.write( "                       \r\n" );
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document.write( "Shade the second one to the right of , because\r\n" );
document.write( "\"greater than\" is \"right\":\r\n" );
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document.write( "x > \r\n" );
document.write( "-----------l-------------l==========>\r\n" );
document.write( "                      \r\n" );
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document.write( "Now since the word between the inequalities is \"OR\" \r\n" );
document.write( "and not \"AND\", we shade all parts of the final\r\n" );
document.write( "number line if it is shaded on the first one OR if \r\n" );
document.write( "it is shaded on the second one.\r\n" );
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document.write( "So the final number line is:\r\n" );
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document.write( "x < or x >  \r\n" );
document.write( "<==========l-------------l==========>\r\n" );
document.write( "                        \r\n" );
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document.write( "Now we imagine that there is a \"negative infinity\"\r\n" );
document.write( "on the far left and an \"infinity\" on the far right.\r\n" );
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document.write( "So the interval notation is\r\n" );
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document.write( "(-oo, ] U [, oo)\r\n" );
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document.write( "Edwin

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