document.write( "Question 1183772: Solve: |x+7| + |x-4| = 13 \n" ); document.write( "
Algebra.Com's Answer #814242 by greenestamps(13203)\"\" \"About 
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\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 \"abs%28x%2B7%29=-%28x%2B7%29=-x-7\"
\n" ); document.write( "and x-4 is also negative, so \"abs%28x-4%29=-%28x-4%29=-x%2B4\"

\n" ); document.write( "and then the equation is
\n" ); document.write( "\"%28-x-7%29%2B%28-x%2B4%29=13\"
\n" ); document.write( "\"-2x-3=13\"
\n" ); document.write( "\"-16=2x\"
\n" ); document.write( "\"x=-8\"

\n" ); document.write( "(2) If x is between -7 and 4, then
\n" ); document.write( "x+7 is positive, so \"abs%28x%2B7%29=x%2B7\"
\n" ); document.write( "and x-4 is negative, so \"abs%28x-4%29=-%28x-4%29=-x%2B4\"

\n" ); document.write( "and then the equation is
\n" ); document.write( "\"%28x%2B7%29%2B%28-x%2B4%29=13\"
\n" ); document.write( "\"11=13\"

\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 \"abs%28x%2B7%29=x%2B7\"
\n" ); document.write( "and x-4 is also positive, so \"abs%28x-4%29=x-4\"

\n" ); document.write( "and then the equation is
\n" ); document.write( "\"%28x%2B7%29%2B%28x-4%29=13\"
\n" ); document.write( "\"2x%2B3=13\"
\n" ); document.write( "\"2x=10\"
\n" ); document.write( "\"x=5\"

\n" ); document.write( "So there are two solutions: x=-8 and x=5.

\n" ); document.write( "Here is a graph of the two functions \"abs%28x%2B7%29%2Babs%28x-4%29\" and \"13\"; the two graphs intersect at x=-8 and x=5.

\n" ); document.write( "\"graph%28400%2C200%2C-10%2C10%2C-5%2C20%2Cabs%28x%2B7%29%2Babs%28x-4%29%2C13%29\"

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