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Given
\n" ); document.write( "(1) 2k - 6 > 3k + 2
\n" ); document.write( "Solve this the same way you would if it was an equation, but follow the properties of ineqaulities.
\n" ); document.write( "First step is to subtract 2k from each side and get
\n" ); document.write( "(2) 2k - 2k - 6 > 3k - 2k + 2 or
\n" ); document.write( "(3) -6 > k + 2
\n" ); document.write( "Now subtract 2 from each side and get
\n" ); document.write( "(4) -6 -2 > k + 2 - 2 or
\n" ); document.write( "(5) -8 > k or
\n" ); document.write( "(6) k < -8
\n" ); document.write( "Let try a couple values k to see if we are correct.
\n" ); document.write( "First let k = -8, then (1) become
\n" ); document.write( "(7) -16 -6 > -24 +2 or
\n" ); document.write( "(8) -22 > -22, which is not true.
\n" ); document.write( "Let try k = -9, then (1) becomes
\n" ); document.write( "(9) -18 - 6 > -27 +2 or
\n" ); document.write( "(10) -24 > -25, which is true
\n" ); document.write( "So k has to be LESS than -8 to satisfy the given inequality of (1). Just to be sure try k = -7, in (1) and get
\n" ); document.write( "(11) -14 -6 > -21 + 2 or
\n" ); document.write( "(12) -20 > -19, which is false (not true)
\n" ); document.write( "Answer: k < -8
\n" ); document.write( "Note: Neither of the arithmetic operations of subtraction in the above steps \"violate\" the properties (rules) of inequalities. \n" ); document.write( "