Subjects algebra

Inequality Pages 69E94B

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1. **State the problem:** We are given the inequality $$2(p + 6) > 20$$ where $p$ represents the number of pages Mr. Vann assigned. 2. **Analyze the inequality:** The expression $2(p + 6)$ means twice the quantity $p + 6$. 3. **Solve the inequality:** $$2(p + 6) > 20$$ Distribute the 2: $$2p + 12 > 20$$ Subtract 12 from both sides: $$2p + \cancel{12} - \cancel{12} > 20 - 12$$ $$2p > 8$$ Divide both sides by 2: $$\frac{2p}{\cancel{2}} > \frac{8}{\cancel{2}}$$ $$p > 4$$ 4. **Interpret the solution:** The number of pages Mr. Vann assigned, $p$, is greater than 4. 5. **Match the scenario:** - The inequality involves $2(p + 6)$, which can be interpreted as twice the number of pages assigned by Mr. Vann plus 6. - The term $p + 6$ suggests someone assigned 6 more pages than Mr. Vann. - The factor 2 outside suggests someone assigned twice as many pages as that person. - The inequality states this quantity is greater than 20. Looking at the options: - "Mr. Shay assigned his class 6 more pages than Mr. Vann. Ms. Tam assigned her class twice as many pages as Mr. Shay. Mr. Vann assigned more than 20 pages of reading." This matches the inequality structure: Ms. Tam's pages = $2(p + 6)$, and this is greater than 20. - The other options do not match the structure of the inequality. **Final answer:** The scenario that matches the inequality is: "Mr. Shay assigned his class 6 more pages than Mr. Vann. Ms. Tam assigned her class twice as many pages as Mr. Shay. Mr. Vann assigned more than 20 pages of reading."