![\"\"](\"/images/stars/stars-13.gif\")
You can put this solution on YOUR website!
.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " I want to show you the short way to solve these problems.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "(1) | x - 3 | - 5 >= 2\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " It is equivalent to this inequality\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " | x - 3 | >= 7.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " The solutions to the last inequality are all numbers in the number line that are remoted from the number 3 to 7 or more units.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " Obviously, these numbers are x >= 3 + 7 = 10 OR x <= 3 - 7 = -4.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " So, the solution to the original inequality is the union of two sets { x <= -4 } and { x >= 10 }. ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " Notice that all absolute value inequalities OF THIS FORM can be easily solved using this chain of arguments.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " See the lesson\r\n" );
document.write( " - Solving absolute value inequalities \r\n" );
document.write( " in this site.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(2) | 2x + 12 | = -6.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " An absolute value of a number is ALWAYS non-negative.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " It can not be negative.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " So, the given equation HAS NO solutions in real number. <<<---=== At this point, the solution is just COMPLETED.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " You can make your conclusion even without writing this absolute value equation in any other form.\r\n" );
document.write( "\r\n" );
document.write( " Moreover, when you make this conclusion without writing this absolute value equation in any other form,\r\n" );
document.write( "\r\n" );
document.write( " you demonstrate that you FIRMLY KNOW what the absolute value is.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " If, in opposite, you try to transform such an equation to any other form, you demonstrate that you are not firm in your knowledge.\r\n" );
document.write( "\r\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Happy learning (!)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Come again soon to the forum to learn something new (!)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "