SOLUTION: Solve: |x+7| + |x-4| = 13

Question 1183772: Solve: |x+7| + |x-4| = 13
Found 3 solutions by MathLover1, greenestamps, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

Solve:

find positive and negative intervals

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): You can put this solution on YOUR website!
.

At this forum, the team of the first class tutors is needed

to neutralize the errors of the rest of the tutors.

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