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Find all $x$ such that both $2x$ and $3x-7$ are in the interval $(-1,12)$.

 Aug 9, 2024
 #1
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We can write down two inequalities and then combine the values of x to get the interval. 

The two inequalities we have are 

1<2x<12     (1)1<3x7<12     (2)

 

Now, let's isolate x from each equation to find the values of x. 

From the first equation, we get that

1/2<x<6

 

From the second equation, we get that

6<3x<192<x<19/3

 

Since we must take the most restrictive interval, the overlapping values of both gets us the interval

2<x<6 or (2,6) in interval notation .

 

Thanks! :)

 Aug 9, 2024
edited by NotThatSmart  Aug 9, 2024

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