1. **State the problem:** We need to write an inequality involving pixels per inch (ppi) that relates the lab's average finger width in pixels to the manufacturers' widths. 2. **Given information:** - Resolution range: $72 \leq \text{ppi} \leq 300$ - Lab's average finger width in pixels: between 45 and 57 pixels - Manufacturer widths: 44 pixels, minimum 26 pixels, minimum 28 pixels 3. **Interpretation:** The lab's average width in pixels is wider than the manufacturers' widths. We want to express this as an inequality involving ppi. 4. **Formulate the inequality:** Since the lab's average width is between 45 and 57 pixels, and this is wider than the manufacturers' widths (44, 26, 28 pixels), the lab's width must be greater than each manufacturer's width. 5. **Write the inequality:** $$ 45 \leq \text{Lab width in pixels} \leq 57 $$ and $$ \text{Lab width} > 44, \quad \text{Lab width} > 26, \quad \text{Lab width} > 28 $$ 6. **Combine the inequalities:** $$ 45 \leq \text{Lab width} \leq 57 \quad \text{and} \quad \text{Lab width} > 44, 26, 28 $$ Since 45 is already greater than 44, 26, and 28, the inequality for the lab's width in pixels is: $$ 45 \leq \text{Lab width} \leq 57 $$ 7. **Relate to pixels per inch:** The lab used 72 ppi to convert finger width to pixels. The inequality for ppi is: $$ 72 \leq \text{ppi} \leq 300 $$ **Final inequality combining all information:** $$ 72 \leq \text{ppi} \leq 300 \quad \text{and} \quad 45 \leq \text{Lab width in pixels} \leq 57 $$