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)![]() ![]() ![]() 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 \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |