Solve for [tex]$ x $[/tex]:

[tex]\[ -7 \ \textless \ x - 1 \ \textless \ 8 \][/tex]

A. [tex]$ 6 \ \textless \ x \ \textless \ 9 $[/tex]
B. [tex]$ -6 \ \textgreater \ x \ \textgreater \ 9 $[/tex]
C. [tex]$ 6 \ \textgreater \ x \ \textgreater \ -9 $[/tex]
D. [tex]$ -6 \ \textless \ x \ \textless \ 9 $[/tex]

Sure! Let's solve the inequality step by step.

We are given the inequality:
[tex]\[ -7 < x - 1 < 8 \][/tex]

Our goal is to solve for [tex]$ x $[/tex].

### Step 1: Isolate [tex]$ x $[/tex]
We start by isolating [tex]$ x $[/tex] in the middle part of the inequality. To do this, we need to get rid of the [tex]$ -1 $[/tex] that is subtracted from [tex]$ x $[/tex].

To remove [tex]$ -1 $[/tex], we will add 1 to all three parts of the inequality.

[tex]\[ -7 + 1 < x - 1 + 1 < 8 + 1 \][/tex]

### Step 2: Simplify the inequality
When we add 1 to each part, we simplify the inequality as follows:

[tex]\[ -7 + 1 = -6 \][/tex]

[tex]\[ x - 1 + 1 = x \][/tex]

[tex]\[ 8 + 1 = 9 \][/tex]

Putting it all together, we now have:

[tex]\[ -6 < x < 9 \][/tex]

### Conclusion
So the solution to the inequality [tex]$ -7 < x - 1 < 8 $[/tex] is:

[tex]\[ -6 < x < 9 \][/tex]

This matches with the option [tex]$ -6 < x < 9 $[/tex], which is the correct answer.

Therefore, the correct answer is [tex]$ -6 < x < 9 $[/tex].