document.write( "Question 48496: solve the absolute value of | 2/3x-2 | - 7 > 2? \n" ); document.write( "

Algebra.Com's Answer #32153 by josmiceli(19441) $\"\"$ $\"About$

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| 2/3 x - 2| - 7 > 2
\n" ); document.write( "add 7 to both sides
\n" ); document.write( "| 2/3 x - 2| > 9
\n" ); document.write( "Let 2/3 x = z
\n" ); document.write( "| z - 2 | > 9
\n" ); document.write( "11 < z < -7
\n" ); document.write( "11 < 2/3 x < -7
\n" ); document.write( "multiply through by 3
\n" ); document.write( "33 < 2x < -21
\n" ); document.write( "divide through by 2
\n" ); document.write( "33/2 < x < -21/2 answer
\n" ); document.write( "check
\n" ); document.write( "Let x = 33/2
\n" ); document.write( "| 2/3 x - 2| - 7 > 2
\n" ); document.write( "|(2/3)(33/2)- 2| - 7 > 2
\n" ); document.write( "|11 - 2| - 7 > 2
\n" ); document.write( "9 - 7 > 2
\n" ); document.write( "2 > 2
\n" ); document.write( "false, so x > 33/2
\n" ); document.write( "Let x = -21/2
\n" ); document.write( "| 2/3 x - 2| - 7 > 2
\n" ); document.write( "| (2/3)(-21/2) - 2| - 7 > 2
\n" ); document.write( "| -7 -2| -7 > 2
\n" ); document.write( "9 - 7 > 2
\n" ); document.write( "2 > 2
\n" ); document.write( "false, so x < -21/2 \n" ); document.write( "

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