To solve the inequality -7 \(\leq\) 9 - 8x < 16 - x, we can start by subtracting 9 from all sides to get:

-16 \(\leq\) -8x < 7 - x

Next, we can add x to all sides to get:

-16 + x \(\leq\) -7x < 7

Now, we can divide all sides by -7, remembering to flip the inequality signs since we are dividing by a negative number:

\(\frac{-16 + x}{-7}\) \(\geq\) x > -1

Simplifying the left side, we get:

\(\frac{x - 16}{-7}\) \(\geq\) x > -1

Multiplying both sides of the left inequality by -7, we get:

x - 16 \(\leq\) -7x > -1

Adding 7x to both sides of the left inequality, we get:

8x - 16 \(\leq\) 0 > -1

Adding 16 to both sides of the left inequality, we get:

8x \(\leq\) 16 > -1

Finally, dividing all sides of the left inequality by 8, we get:

x \(\leq\) 2 > -1

So the solution to the inequality is: -1 < x \(\leq\) 2.