document.write( "Question 1139391: Solution set and graph for...
\n" ); document.write( "| 2 ( | x - 3 | ) - 7 | < 5 \n" ); document.write( "
Algebra.Com's Answer #759869 by greenestamps(13200)\"\" \"About 
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\n" ); document.write( "Plan:
\n" ); document.write( "Find the solution set for equal to 5;
\n" ); document.write( "then use end behavior to determine when the inequality is true.
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document.write( "\"abs%282%2Aabs%28x-3%29-7%29+=+5\"  -->  (1) \"2%2Aabs%28x-3%29-7+=+5\"  OR  (2) \"2%2Aabs%28x-3%29-7+=+-5\"\r\n" );
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document.write( "(1):\r\n" );
document.write( "\"2%2Aabs%28x-3%29-7+=+5\"\r\n" );
document.write( "\"2%2Aabs%28x-3%29+=+12\"\r\n" );
document.write( "\"abs%28x-3%29+=+6\"  -->  (1a) \"x-3+=+6\"  OR  (1b) \"x-3+=+-6\"\r\n" );
document.write( "(1a):  \"x-3+=+6\"  -->  \"x+=+9\"\r\n" );
document.write( "(1b):  \"x-3+=+-6\"  -->  \"x+=+-3\"\r\n" );
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document.write( "(2):\r\n" );
document.write( "\"2%2Aabs%28x-3%29-7+=+-5\"\r\n" );
document.write( "\"2%2Aabs%28x-3%29+=+2\"\r\n" );
document.write( "\"abs%28x-3%29+=+1\"  -->  (1a) \"x-3+=+1\"  OR  (1b) \"x-3+=+-1\"\r\n" );
document.write( "(1a):  \"x-3+=+1\"  -->  \"x+=+4\"\r\n" );
document.write( "(1b):  \"x-3+=+-1\"  -->  \"x+=+2\"\r\n" );
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\n" ); document.write( "We are done with the first step: the values of x for which the expression is equal to 5 are -3, 2, 4, and 9. Now for the second step.

\n" ); document.write( "1) The value of the expression is always 0 or positive, because it is an absolute value.
\n" ); document.write( "2) For large positive or large negative values of x, the value of the expression will be large.
\n" ); document.write( "3) Every segment of the graph is linear.

\n" ); document.write( "Given those three facts and the four values of x for which the expression is equal to 5, we can conclude that the inequality (value of the expression is less than 5) is true between x = -3 and x = 2, and between x = 4 and x = 9.

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\n" ); document.write( "ANSWER: The solution set for the inequality is (-3,2) U (4,9)

\n" ); document.write( "A graph:

\n" ); document.write( "\"graph%28400%2C400%2C-10%2C15%2C-5%2C15%2Cabs%282%2Aabs%28x-3%29-7%29%2C5%29\" \n" ); document.write( "
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