I am preparing for GRE. These two problems are from Manhattan 5lb book. I am finding absolute value equations very daunting. Sometimes it is time consuming, sometimes it seems very difficult to me. Following two are comparison problems. You have to compare quantity A with quantity B (i.e. if Quantity A> Quantity B, Quantity A< Quantity B, Quantity A= Quantity B, or it cannot be determined from the given information ) 

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> Prolblem 1:
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If $p+|k|>|p|+k$, compare

Quantity A: $p$

Quantity B: $k$

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> Problem 2:
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If $|x|+|y|>|x+z|$, compare

Quantity A: $y$

Quantity B: $z$

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> My solution approach
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a) p $(+ve)$ and k $(+ve)$ --> not possible 

b) p $(+ve)$ and k $(-ve)$ --> possible (In this case, Quantity A> Quantity B)

c) p $(-ve)$ and k $(+ve)$ --> not possible 

d) p $(-ve)$ and k $(-ve)$ --> possible if $|k|>|p$| (In this case, Quantity A> Quantity B)

e) p =0 and k $(+ve)$ --> not possible

f) p =0 and k $(-ve)$ --> possible (In this case, Quantity A> Quantity B)

g) p $(+ve)$ and k =0, --> not possible

h) p $(-ve)$ and k =0, --> not possible

In all three possible cases, Quantity A> Quantity B. so, Quantity A> Quantity B is the answer.

I also solve problem 2 in a similar way. Can you show me the easier approach or the right approach to deal with these problems?