\( \operatorname{Let} y=8 \) 1. \( 35-3 y \) 2. \( 9+6 y-18 \) 3. \( y^{2}-7 \times 2 \) Let \( c=3 \) 6. \( 8(10 c-25) \) 4. \( \left(s+c^{3}\right)-14 \) 5. \( 4 c-6 * 3 \)
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The Deep Dive
To dive into some historical context, did you know that mathematical expressions like these have roots dating back to ancient civilizations? The Babylonians, for instance, were solving equations nearly 4,000 years ago using a numerical system that laid the groundwork for algebra as we know it. Their methods were often based on geometric interpretations, making them quite advanced for their time! When it comes to applying these calculations in real world scenarios, think about budgeting! If you adjust your expenses based on changing variables (like the cost of food or entertainment), you're effectively using algebra to solve for your budget. Whether you're figuring out how much you can spend after certain bills or planning savings goals, these calculations help you maintain financial balance and make informed decisions!