document.write( "Question 1192806: Solve the inequalities for the range of x if any.
\n" ); document.write( "|x|+|2-x|<2 \n" ); document.write( "

Algebra.Com's Answer #824712 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Use the definition of absolute value \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Isolate the more complicated square root on the left:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Square both sides:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by -4 which flips the < to >:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "This can never be true because if x were positive,\r\n" );
document.write( "equality would hold.   If x were 0, equality would\r\n" );
document.write( "hold, and if x were negative, < would hold.\r\n" );
document.write( "\r\n" );
document.write( "So the inequality is a contradiction.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );