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Find the interval of all $x$ such that both $2x$ and $3x$ are in the interval $(1,2)$.

 May 29, 2019
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1 < 2x < 2      divide through by 2

 

1/2 < x < 1

 

Also

 

1 < 3x < 2      divide through by 3

 

1/3 < x < 2/3

 

We need the most restrictive interval that solves both of these inequalities....this is  (1/2 , 2/3)

 

 

 

cool cool cool

 May 29, 2019
edited by CPhill  May 29, 2019

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