document.write( "Question 1183772: Solve: |x+7| + |x-4| = 13 \n" ); document.write( "
Algebra.Com's Answer #814242 by greenestamps(13203)![]() ![]() You can put this solution on YOUR website! \n" ); document.write( "(Revised/expanded response, following comment from student....) \n" ); document.write( "The solution from the other tutor arrives at the correct solution. However, the method of solution is deficient; and the limited explanation of HOW to solve the problem makes the response of little use to the student. \n" ); document.write( "The function changes behavior at x=-7 and x=4; so three intervals must be examined for solutions: x less than -7, x between -7 and 4, and x greater than 4. \n" ); document.write( "(1) If x is less than -7, then \n" ); document.write( "x+7 is negative, so \n" ); document.write( "and x-4 is also negative, so \n" ); document.write( "and then the equation is \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "(2) If x is between -7 and 4, then \n" ); document.write( "x+7 is positive, so \n" ); document.write( "and x-4 is negative, so \n" ); document.write( "and then the equation is \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "That equation is obviously never true, so there is no solution in the interval between -7 and 4. \n" ); document.write( "(3) If x is greater than 4, then \n" ); document.write( "x+7 is positive, so \n" ); document.write( "and x-4 is also positive, so \n" ); document.write( "and then the equation is \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "So there are two solutions: x=-8 and x=5. \n" ); document.write( "Here is a graph of the two functions \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " |