document.write( "Question 1207257: How many integers satisfy |x+1|<4 \n" ); document.write( "
Algebra.Com's Answer #845021 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "Answer: 7\r
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\n" ); document.write( "\n" ); document.write( "Work Shown\r
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\n" ); document.write( "\n" ); document.write( "|x+1| < 4
\n" ); document.write( "-4 < x+1 < 4
\n" ); document.write( "-4-1 < x+1-1 < 4-1
\n" ); document.write( "-5 < x < 3\r
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\n" ); document.write( "\n" ); document.write( "In the 2nd step I used the rule that |x| < k leads to -k < x < k for some positive real number k.\r
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\n" ); document.write( "\n" ); document.write( "-5 < x < 3 means that x is between -5 and 3 excluding both endpoints.
\n" ); document.write( "If x was an integer then x can be selected from the set {-4, -3, -2, -1, 0, 1, 2}
\n" ); document.write( "There are 7 integers listed in that set.\r
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\n" ); document.write( "\n" ); document.write( "Example: Let's check x = -2
\n" ); document.write( "|x+1| < 4
\n" ); document.write( "|-2+1| < 4
\n" ); document.write( "|-1| < 4
\n" ); document.write( "1 < 4
\n" ); document.write( "That works out.
\n" ); document.write( "I'll let the student check the other integer solutions.
\n" ); document.write( "Now let's try a non-solution such as x = 5
\n" ); document.write( "|x+1| < 4
\n" ); document.write( "|5+1| < 4
\n" ); document.write( "|6| < 4
\n" ); document.write( "6 < 4
\n" ); document.write( "Which is false so x = 5 is confirmed to be not part of the solution set.
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