document.write( "Question 1208929: If |x + 1| <= 3, then a <= 1/(x + 5) <= b.
\n" ); document.write( "Find a and b.\r
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Algebra.Com's Answer #847475 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The prescribed values for x are defined by

\n" ); document.write( " $\"abs%28x%2B1%29%3C=3\"$
\n" ); document.write( " $\"-3%3C=x%2B1%3C=3\"$
\n" ); document.write( " $\"-4%3C=x%3C=2\"$

\n" ); document.write( "The interval of x values is thus [-4,2].

\n" ); document.write( "For all the values of x in that interval, x+5 is positive, so 1/(x+5) is positive and monotonically decreasing. So the maximum value of 1/(x+5) on [-4,2] is at the left end of the interval and the minimum value is at the right end of the interval.

\n" ); document.write( "ANSWERS:

\n" ); document.write( "a = minimum value = 1/(2+5) = 1/7
\n" ); document.write( "b = maximum value = 1/(-4+5) = 1/1 = 1

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