Let's solve the inequality step by step:

$16x - 7 \leq -71$

Step 1: Add 7 to both sides to isolate the term with $x$.

$16x - 7 + 7 \leq -71 + 7$

This simplifies to:

$16x \leq -64$

Step 2: Divide both sides by 16 to solve for $x$.

$x \leq \frac{-64}{16}$

$x \leq -4$

Thus, the solution to the inequality is:

$x \leq -4$

Solution: $x \leq -4$

Would you like more details on this or have any questions?

Here are some related problems for practice:

1. Solve: $12x + 5 \geq -19$
2. Solve: $8x - 10 \leq 6$
3. Solve: $5x - 3 > -18$
4. Solve: $3x + 4 \leq 16$
5. Solve: $-9x + 7 \geq 34$

Tip: When solving inequalities, remember that if you multiply or divide both sides by a negative number, the inequality sign flips!