document.write( "Question 793359: -5 < 2(2-s) + 1 ≤ 9 \n" ); document.write( "
Algebra.Com's Answer #480342 by DrBeeee(684)\"\" \"About 
You can put this solution on YOUR website!
Given:
\n" ); document.write( "(1) \"-5%3C2%2A%282-s%29%2B1%3C=9\"
\n" ); document.write( "This is a \"two sided\" inequality which will give an interval space for the possible values of the variable, s in this case. The solution is straight forward - you solve each \"side\" separately as follows.
\n" ); document.write( "First solve the left side inequality given by
\n" ); document.write( "(2)\"-5%3C2%2A%282-s%29%2B1\" or
\n" ); document.write( "(3)\"-5%3C2%2A2-2%2As%2B1\" or
\n" ); document.write( "(4)\"-5%3C4-2%2As%2B1\" or
\n" ); document.write( "(5)\"-5%3C5-2%2As\" or
\n" ); document.write( "(6)\"2%2As%3C5%2B5\" or
\n" ); document.write( "(7)\"2%2As%3C10\" or
\n" ); document.write( "(8)\"s%3C5\"
\n" ); document.write( "Now solve the right half of the inequality
\n" ); document.write( "(9)\"2%2A%282-s%29%2B1%3C=9\"
\n" ); document.write( "(10)\"4-2%2As%2B1%3C=9\"
\n" ); document.write( "(11)\"5-2%2As%3C=9\"
\n" ); document.write( "(12)\"-2%2As%3C=4\"
\n" ); document.write( "(13)\"-4%3C=2%2As\"
\n" ); document.write( "(14)\"-2%3C=s\"
\n" ); document.write( "Our two sided answer is given by (14) and (8) as
\n" ); document.write( "(15)\"-2%3C=s%3C5\"
\n" ); document.write( "If you put the limits of (15) into (1) you should get the two sided limits of (1).
\n" ); document.write( "When s = -2 in (1) we get
\n" ); document.write( "(16)\"-5%3C2%2A%282%2B2%29%2B1%3C=9\" or
\n" ); document.write( "(17)\"-5%3C8%2B1%3C=9\"
\n" ); document.write( "(18)\"-5%3C9%3C=9\"
\n" ); document.write( "When s = 5 in (1) we get
\n" ); document.write( "(19)\"-5%3C2%2A%282-5%29%2B1%3C=9\" or
\n" ); document.write( "(20)\"-5%3C-6%2B1%3C=9\" or
\n" ); document.write( "(21)\"-5%3C-5%3C=9\"
\n" ); document.write( "Answer: \"-2%3C=s%3C5\"\r
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