Question 1183772: Solve: |x+7| + |x-4| = 13
Found 3 solutions by MathLover1, greenestamps, ikleyn:
Answer by MathLover1(20850)   (Show Source):
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
(Revised/expanded response, following comment from student....)
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.
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.
(1) If x is less than -7, then
x+7 is negative, so 
and x-4 is also negative, so 
and then the equation is
(2) If x is between -7 and 4, then
x+7 is positive, so 
and x-4 is negative, so
and then the equation is
That equation is obviously never true, so there is no solution in the interval between -7 and 4.
(3) If x is greater than 4, then
x+7 is positive, so
and x-4 is also positive, so 
and then the equation is
So there are two solutions: x=-8 and x=5.
Here is a graph of the two functions  and  ; the two graphs intersect at x=-8 and x=5.
Answer by ikleyn(52834)  (Show Source):
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