The inequality you're working with is:

$3x - 7 \leq -22$

Let's solve for $x$:

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

$3x - 7 + 7 \leq -22 + 7$

$3x \leq -15$

2. Divide both sides by 3:

$x \leq \frac{-15}{3}$

$x \leq -5$

Thus, the solution is:

$x \leq -5$

Let me know if you need any more details or explanations!

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Here are 5 related questions you can try:

1. Solve: $4x - 9 \geq -13$
2. Solve: $2x + 5 \leq -3$
3. Solve: $-5x + 4 > -21$
4. Solve: $6x - 8 \leq 10$
5. Solve: $9x - 6 \geq 12$

Tip: When dividing or multiplying both sides of an inequality by a negative number, remember to reverse the inequality sign.