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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.

 Jun 3, 2024
 #1
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2 -4z < -7      2 -4z > 13

9 < 4z           -11 > 4z

z > 9/4            z < -11/4

 

So....for the first one

(-inf, -11/4) U ( 9/4, inf)

 

2 + 7z < -7        2 +  7z > 13

7z < -9               7z > 11

z < -9/2               z > 11/7

 

So.... for the second one

(inf, -9/2) U (11/7, inf)

 

The most restrictive intervals are

 

(inf, -9/2) U ( 9/4 ,inf )

 

cool cool cool

 Jun 3, 2024

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