7 Reese has enough money to buy 115 cm of framing. He wants the frame to be at least 28.5 cm long. Write and solve an inequality to find the possible widths, w, for the frame that Reese can construct. Inequality: Solution:

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To determine the possible widths $$ w $$ that Reese can use for his frame, we'll set up and solve an inequality based on the information provided.

### **Inequality:**
$$ 2L + 2w \leq 115 $$

### **Explanation:**
1. **Understanding the Problem:**
   - **Total framing available:** 115 cm
   - **Minimum length of the frame ($$ L $$):** 28.5 cm
   - **Width of the frame ($$ w $$):** To be determined

2. **Setting Up the Inequality:**
   - For a rectangular frame, the perimeter $$ P $$ is given by:
     $$ P = 2L + 2w $$
   - Reese has at most 115 cm of framing, so:
     $$ 2L + 2w \leq 115 $$

3. **Substituting the Minimum Length:**
   - Given $$ L \geq 28.5 $$ cm, we'll substitute $$ L = 28.5 $$ cm to find the maximum possible width:
     $$ 2(28.5) + 2w \leq 115 $$
     $$ 57 + 2w \leq 115 $$

4. **Solving for $$ w $$:**
   $$ 2w \leq 115 - 57 $$
   $$ 2w \leq 58 $$
   $$ w \leq 29 $$

### **Solution:**
The possible width $$ w $$ that Reese can use for his frame must satisfy:
$$ w \leq 29 \text{ cm} $$

This means Reese can choose any width up to **29 cm** to construct his frame while staying within his budget for the framing material.

**Final Answer:**

**Inequality:**
$$ 2(28.5) + 2w \leq 115 $$

**Solution:**
$$ w \leq 29 \text{ cm} $$
The possible width $$ w $$ for Reese's frame must be less than or equal to 29 cm.

7 Reese has enough money to buy 115 cm of framing. He wants the frame to be at least 28.5 cm long. Write and solve an inequality to find the possible widths, w, for the frame that Reese can construct. Inequality: Solution:

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