$$ |2 w-5| \leq 9 $$ Select the correct choice below and fill in any answer boxes present in your choice. A. The solution set is $$ \{w \mid w \leq \square $$ or $$ w \geq \square\} $$. (Simplify your answers.) B. The solution set is $$ \{w \mid \square \leq w \leq \square\} $$. (Simplify your answers.) C. The solution set is all real numbers. D. The solution is the empty set.

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To solve the inequality $$ |2w - 5| \leq 9 $$, we follow these steps:

1. **Understand the Absolute Value Inequality:**
   
   The inequality $$ |2w - 5| \leq 9 $$ means that the expression inside the absolute value, $$2w - 5$$, is at most 9 units away from 0. This can be translated into a compound inequality:
   
   $$
   -9 \leq 2w - 5 \leq 9
   $$

2. **Solve the Compound Inequality:**

- **Add 5 to all parts of the inequality:**
     
     $$
     -9 + 5 \leq 2w \leq 9 + 5
     $$
     
     $$
     -4 \leq 2w \leq 14
     $$
   
   - **Divide all parts by 2 to solve for $$w$$:**
     
     $$
     \frac{-4}{2} \leq w \leq \frac{14}{2}
     $$
     
     $$
     -2 \leq w \leq 7
     $$

3. **Express the Solution Set:**

The solution set is all real numbers $$w$$ such that $$w$$ is between $$-2$$ and $$7$$, inclusive. This matches **Choice B**.

$$
   \{w \mid -2 \leq w \leq 7\}
   $$

**Final Answer:**

**B.** The solution set is $$ \{w \mid -2 \leq w \leq 7\} $$.
The solution set is all real numbers $$ w $$ such that $$ -2 \leq w \leq 7 $$.

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