https://file.aiquickdraw.com/mathbot/file/1726151031909tgqt14vr.jpg

Let's solve the inequality step by step.

The given inequality is:
\[
-2(w + 5) + 9 < -11
\]

### Step 1: Distribute the \(-2\)
\[
-2(w + 5) = -2w - 10
\]
So the inequality becomes:
\[
-2w - 10 + 9 < -11
\]

### Step 2: Combine like terms
\[
-2w - 1 < -11
\]

### Step 3: Add 1 to both sides
\[
-2w < -10
\]

### Step 4: Divide both sides by \(-2\) and reverse the inequality sign (since we're dividing by a negative number)
\[
w > 5
\]

So, the solution is \( w > 5 \), which corresponds to **option D** in the provided answer choices.

Would you like further details or have any questions?

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Here are five related questions to practice:
1. How do you solve inequalities with fractions?
2. What is the difference between solving an equation and an inequality?
3. How do you graph the solution of an inequality on a number line?
4. What happens when you multiply or divide an inequality by a negative number?
5. How can you check if a solution to an inequality is correct?

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

Solve the inequality. Graph the solution. -2(w + 5) + 9 < -11

Step-by-step solution for solving the inequality -2(w + 5) + 9 < -11, using algebraic techniques like distribution and properties of inequalities. Understand how to graph the solution w > 5. Suitable for Grades 7-9 students learning algebra.

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