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The inequality you provided is:

\[
-3(w + 5) + 9 < -18
\]

Let's solve it step-by-step:

### Step 1: Expand the expression
Distribute \(-3\) across \((w + 5)\):
\[
-3w - 15 + 9 < -18
\]

### Step 2: Simplify
Combine the constant terms:
\[
-3w - 6 < -18
\]

### Step 3: Isolate the variable term
Add 6 to both sides to move the constant to the right-hand side:
\[
-3w < -18 + 6
\]
\[
-3w < -12
\]

### Step 4: Solve for \(w\)
Divide both sides by \(-3\). Remember that dividing by a negative number reverses the inequality sign:
\[
w > 4
\]

### Final solution:
\[
w > 4
\]

This is the solution to the inequality.

Would you like further details or have any questions about this solution? Here are some related questions to explore:

1. How do you solve inequalities when there are fractions involved?
2. What happens to the inequality sign when multiplying or dividing by a negative number?
3. How do you graph the solution of an inequality on a number line?
4. What are the differences between solving equations and inequalities?
5. Can you solve a compound inequality, such as \(5 < 2x + 1 \leq 11\)?

**Tip:** Always remember to reverse the inequality sign when dividing or multiplying by a negative number!

This problem involves solving the inequality -3(w + 5) + 9 < -18. Learn how to use the distributive property, simplify expressions, and correctly handle inequalities when dividing by negative numbers. Suitable for students in Grades 7-10.

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