document.write( "Question 1124511: how many solution does the equation a|x+b|+c=d have if a < 0 and c = d? If a < 0, d > 0 and c < d ? Explain \n" ); document.write( "
Algebra.Com's Answer #740857 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "how many solution does the equation a|x+b|+c=d have if a < 0 and c = d? If a < 0, d > 0 and c < d ? Explain
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(a)   How many solution does the equation a|x+b|+c=d have if a < 0 and c = d ?\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "An equation\r\n" );
document.write( "\r\n" );
document.write( "    a|x+b| + c = d   \r\n" );
document.write( "\r\n" );
document.write( "is equivalent to\r\n" );
document.write( "\r\n" );
document.write( "    a|x+b| = d - c.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "If c = d, then this equation becomes\r\n" );
document.write( "\r\n" );
document.write( "    a|x+b| = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "If a =/= 0  (as it is given in our case), then the last equation implies\r\n" );
document.write( "\r\n" );
document.write( "   |x+b| = 0,\r\n" );
document.write( "\r\n" );
document.write( "which has one and only one unique solution  x= -b.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  In this case the original equation has a unique solution.\r\n" );
document.write( "
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(b)   How many solution does the equation a|x+b|+c=d have if a < 0, d > 0 and c < d ?\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "An equation\r\n" );
document.write( "\r\n" );
document.write( "    a|x+b| + c = d   \r\n" );
document.write( "\r\n" );
document.write( "is equivalent to\r\n" );
document.write( "\r\n" );
document.write( "    a|x+b| = d - c.     (*)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "If c < d, then the right side of the last equation is positive, while its left side is negative.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Therefore, the equality (*) is not possible.\r\n" );
document.write( "\r\n" );
document.write( "Or, in other words, the equation (*) has no solutions.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  Under the given condition, the given equation has no solution.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved, answered and explained.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );