document.write( "Question 860174: Solve the inequality 2x - 3 < x + 2 ≤ 3x + 5, Can you show your work if possible, thanks! \n" ); document.write( "
Algebra.Com's Answer #518274 by DrBeeee(684)\"\" \"About 
You can put this solution on YOUR website!
This is one of my favorites and the solution is straight forward and something you need to remember.
\n" ); document.write( "Given:
\n" ); document.write( "(1) 2x - 3 < x + 2 <= 3x + 5
\n" ); document.write( "You solve this using the \"left-side inequality\" then the \"right-side inequality\". That is we write (1) as TWO inequalities;
\n" ); document.write( "(2) 2x - 3 < x + 2 and
\n" ); document.write( "(3) x + 2 <= 3x + 5
\n" ); document.write( "Now solve for x in (2).
\n" ); document.write( "(4) 2x - x < 2 + 3 or
\n" ); document.write( "(5) x < 5
\n" ); document.write( "Now solve for x in (3).
\n" ); document.write( "(6) 2 - 5 <= 3x - x or
\n" ); document.write( "(7) -3 <= 2x or
\n" ); document.write( "(8) -3/ <= x
\n" ); document.write( "Now recombine (5) and (7), keeping the order least to most left-to-right
\n" ); document.write( "(9) -3/2 <= x < 5
\n" ); document.write( "Answer: the solution to the inequality is -3/2 <= x < 5.
\n" ); document.write( "Thanks for reading
\n" ); document.write( "Now remember, solve two simple inequalities instead of staring at it and saying \"What'll I do?\"
\n" ); document.write( "PS You can also do this for longer strings of inequalities!\r
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