Find all $z$ such that neither $2+z-5z$ nor $2-z+8z$ is in the interval $(-7,13]$. Express your answer as an interval or as a union of intervals.
2 + z - 5z = 2 - 4z
2 - z + 8z = 2 +7z
2-4z < -7 2 - 4z > 13 2 + 7z < -7 2 + 7z > 13
9 < 4z -11 > 4z 7z < -9 7z > 11
z > 9/4 z < -11/4 z < -9/7 z > 11/7
The most restricitve intervals are
(-inf , -11/4) U (9/4 , inf)
+1323 
