document.write( "Question 1190064: Solve |b-7|< 6
\n" ); document.write( "a. 1>b>13
\n" ); document.write( "b. b>1
\n" ); document.write( "c. 1< b<13 \n" ); document.write( "
Algebra.Com's Answer #821622 by math_tutor2020(3817)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "The handy rule to memorize is
\n" ); document.write( "|x| < k is the same as -k < x < k
\n" ); document.write( "where k is some positive number
\n" ); document.write( "If k was negative, then |x| < k has no solutions. Why? Because |x| itself is never negative, so there's no way |x| is smaller than any negative number.\r
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\n" ); document.write( "\n" ); document.write( "Some examples
  • |x| < 5 becomes -5 < x < 5
  • |3y-1| < 10 is the same as -10 < 3y-1 < 10
  • |w+4| < 7 turns into -7 < w+4 < 7
  • |10n-22| < -55 has no solutions
With all that in mind, let's solve this current inequality
\n" ); document.write( "|b-7| < 6
\n" ); document.write( "-6 < b-7 < 6 ... use the rule mentioned above
\n" ); document.write( "-6+7 < b-7+7 < 6+7 .... adding 7 to all sides
\n" ); document.write( "1 < b+0 < 13
\n" ); document.write( "1 < b < 13\r
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\n" ); document.write( "\n" ); document.write( "The value b is some number between 1 and 13, excluding both endpoints.\r
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\n" ); document.write( "\n" ); document.write( "The graph will have open holes at 1 and 13 on the number line.
\n" ); document.write( "Then you shade between those open holes. This visually describes the interval 1 < b < 13.\r
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\n" ); document.write( "\n" ); document.write( "Answer: Choice C. 1 < b < 13
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