![\"\"](\"/images/stars/stars-11.gif\")
You can put this solution on YOUR website!
Please refer to other solutions using absolute value.
\n" ); document.write( "The \"trick\" is to make the following substitution;
\n" ); document.write( "(1) |y| = y when y>=0 and
\n" ); document.write( "(2) |y| = -y when y<=0
\n" ); document.write( "For your problem, (1) becomes
\n" ); document.write( "(3) 4 - x = +(2 - 3x) when 2 - 3x > 0 or
\n" ); document.write( "(4) 4 - x = +(2 - 3x) when 2 > 3x or
\n" ); document.write( "(5) 4 - x = +(2 - 3x) when x < 2/3
\n" ); document.write( "Now solve (5) for x and get
\n" ); document.write( "(6) 4 - x = 2 - 3x or
\n" ); document.write( "(7) 2 = -2x or
\n" ); document.write( "(8) x = -1
\n" ); document.write( "And since -1 < 2/3 the solution is x = -1.
\n" ); document.write( "For the other condition given by (2) we have
\n" ); document.write( "(9) 4 - x = -(2 - 3x) when 2 - 3x < 0 or
\n" ); document.write( "(10) 4 - x = -(2 - 3x) when 2 < 3x or
\n" ); document.write( "(11) 4 - x = -(2 - 3x) when x > 2/3
\n" ); document.write( "Now solve (11) for x and get
\n" ); document.write( "(12) 4 - x = -2 + 3x or
\n" ); document.write( "(13) 6 = 4x or
\n" ); document.write( "(14) x = 3/2
\n" ); document.write( "And since 3/2 > 2/3 the solution is x = 3/2.
\n" ); document.write( "Answer: x = -1 when x < 2/3, and x = 3/2 when x > 2/3
\n" ); document.write( "How about when x = 2/3? The answer can be -1 or 3/2 depending on the \"side\" of 2/3 that x is an infinitesimal distance from 2/3. If x was greater than 2/3 before it equaled 2/3 the answer is 3/2. If it was less than 2/3 before it equaled 2/3 the answer is -1. The point x = 2/3 is called a point of discontinuity. x \"jumps from -1 to 3/2 instantaneously (zero distance) as x increases from <2/3 to x>2/3.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "