document.write( "Question 903850: 5-2x|≤4 \r
\n" ); document.write( "\n" ); document.write( "5-2x≤4......or.....5-2x≥-4
\n" ); document.write( "-2x≤-1..............-2x≥-9
\n" ); document.write( "x≥1/2................x≤9/2 \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I understand that what I don't understand is how x≥1/2 or x≤9/2 can then be translated to mean 1/2≤x≤9/2....how do the signs change to be both in the same direction when they were both in opposite directions. Please help explain this to me.
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #548344 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
That \"or\" should be \"and\". This is because |x| < k turns into \"x < k and x > k\" for some positive number k.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You should end up with \"x≥1/2 and x≤9/2\" (again notice the \"and\")\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Combining the two gives you 1/2≤x≤9/2\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Side Note: x≥1/2 is the same as 1/2≤x. Everything is just flipped. \n" ); document.write( "

\n" );