#1**+1 **

We can write down two inequalities and then combine the values of x to get the interval.

The two inequalities we have are

\(-1 < 2x < 12 \space \space \space \space \space(1) \\ -1 < 3x - 7 < 12 \space \space \space \space \space (2) \)

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

\( 6 < 3x < 19 \\ 2 < x < 19 / 3\)

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! :)

NotThatSmart Aug 9, 2024