document.write( "Question 1049247: |x+2|<2x+7 \n" ); document.write( "

Algebra.Com's Answer #664841 by ikleyn(52864) $\"\"$ $\"About$

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\n" ); document.write( "|x+2|<2x+7.
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\n" ); document.write( "\n" ); document.write( "|x+2|<2x+7. (1)\r
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document.write( "1.  If x+2 >= 0, then  |x+2| = x+2.\r\n" );
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document.write( "    Hence, in the domain x >= -2 the inequality (1) takes the form\r\n" );
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document.write( "    x + 2 < 2x + 7,   or  2-7 < x,  which is  x > -5.\r\n" );
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document.write( "    In other words, in the domain x >= -2 the solution set is x > -5.\r\n" );
document.write( "    Thus for the domain x > -2 the solution set is the intersection [,)  and  (,), i.e.  [,).\r\n" );
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document.write( "2.  If x+2 < 0, then  |x+2| = -(x+2).\r\n" );
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document.write( "    Hence, in the domain x < -2 the inequality (1) takes the form\r\n" );
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document.write( "    -(x + 2) < 2x + 7,   or  -x - 2 < 2x +7,  or  -2-7 < 3x,  or  -9 < 3x, which is  x > -3.\r\n" );
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document.write( "    In other words, in the domain x < -2 the solution set is x > -3.\r\n" );
document.write( "    Thus for the domain x < -2 the solution set is the intersection (,)  and  (,), i.e.  (,).\r\n" );
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document.write( "3.  Finally, combining these two cases, we obtain the solution set as  (,) U [,,  i.e.  (,).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. The solution set to inequality (1) is ( $\"-3\"$ , $\"infinity\"$ ).\r
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\n" ); document.write( "\n" ); document.write( "Plots y = |x+2| and y = 2x+7\r
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