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.

Learn how to solve the linear inequality 3x - 7 ≤ -22 step by step. This solution demonstrates how to manipulate inequalities, including adding values and dividing by constants. Suitable for students in Grades 7-8.

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