Find the sum of values of $x$ such that $|x+2| +|x-3| +|x+4| + |x+5| = 18$ I tried it by finding the different values at the $4$ inflection points of the graph. Then didn't know how to proceed. Am I correct till here?

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*$x \le -5 $ We need to solve $-(x+2)-(x-3)-(x+4)-(x+5)=18$ 

*$-5 \le x \le -4 $ We need to solve $-(x+2)-(x-3)-(x+4)+(x+5)=18$ 

*$-4 \le x \le -2$ We need to solve $-(x+2)-(x-3)+(x+4)+(x+5)=18$ 

*$-2 \le x \le 3$ We need to solve $(x+2)-(x-3)+(x+4)+(x+5)=18$ 

*$x \ge 3$ We need to solve $(x+2)+(x-3)+(x+4)+(x+5)=18$


Remember solve each of these and see if they are actually s solution to the original equation or even a contradiction with the inequality for that case equation. Hope this helps. 
