Official explanationFrom z < y - x, the value of z depends on x and y. So, solve for x and y as much as possible. There are two cases for the absolute value equation: |x + y| = 10 means that (x + y) = ± 10. Consider these two cases separately

The positive case:x + y = 10, so y = 10 - x. Substitute into z < y - x, getting z < (10 - x) - x, or z < 10 - 2x. Because x is at least zero, 10 - 2x 10. Putting the inequalities together, z < 10 - 2x 10. Thus, z < 10.

The negative case:x + y = -10, so y = -10 - x. Substitute into z < y - x, getting z < (-10 - x) - x, or z < -10 - 2x. Because x is at least zero, -10 - 2x -10. Putting the inequalities together, z < -10 - 2x -10. Thus, z < -10.

In both cases, 10 is greater than z. The correct answer is

(B).
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