$a + (a + 2d) = 14$ → $2a + 2d = 14$ → $a + d = 7$ - Belip
Understanding the Equation $ a + (a + 2d) = 14 $: Simplifying to $ a + d = 7 $
Understanding the Equation $ a + (a + 2d) = 14 $: Simplifying to $ a + d = 7 $
Solving mathematical equations is a fundamental skill in algebra, and simplifying expressions plays a vital role in making complex problems easier to work with. One such example is the equation:
$$
a + (a + 2d) = 14
$$
Understanding the Context
This equation appears simple at first glance, but understanding each step of its transformation reveals powerful insights into algebraic manipulation and simplification. Let’s walk through the process step-by-step and explore why simplifying it to $ a + d = 7 $ is both elegant and valuable.
Step 1: Expand the Parentheses
Start by removing the parentheses using the distributive property:
$$
a + a + 2d = 14
$$
Image Gallery
Key Insights
Step 2: Combine Like Terms
Combine the like terms $ a + a = 2a $:
$$
2a + 2d = 14
$$
Step 3: Factor Out the Common Term
Notice that both terms have a common factor of 2. Factor it out:
🔗 Related Articles You Might Like:
📰 love between fairy and devil 📰 collaboration synonym 📰 2011 hyundai sonata 📰 Pet Lab Roblox 1405289 📰 Saints Vs Jets 3700682 📰 Butter Substitute For Cookies 91031 📰 Claim Stunning Smiles With Gold Teeth Groundbreaking Transformation That Stuns Everyone 946039 📰 1981 Camaro 5562755 📰 Uconn Womens Basketball Transfer Portal 8975473 📰 Gamers Go Wild Ps Plus Extra Delivery Includes Sweeping New Perks 9452354 📰 Cast Jungle Fever 2002569 📰 Watch The Shock That Changes Everything In Step Up 3 4732648 📰 Bass Akustik 1471200 📰 Inside The Royal Pizzerija Shocking Royals Hidden Menu That Changed Everything Forever 917838 📰 Nueces River 7856337 📰 Inside The Inspector General Office Shocking Truths That Shook The Government 6768845 📰 The Good Place Actors Their Secret Superpowers That Made Them Unforgettable 8485007 📰 Trey Hendrickson Stats 3017772Final Thoughts
$$
2(a + d) = 14
$$
Step 4: Solve for $ a + d $
Divide both sides by 2:
$$
a + d = 7
$$
Why Simplifying Matters
Even though the original equation appears more complex, the simplified form, $ a + d = 7 $, reveals a clean linear relationship between variables $ a $ and $ d $. This form is useful because:
- Easier Computation: Working with $ a + d = 7 $ allows faster calculations without extraneous terms.
- Greater Flexibility: You can express one variable in terms of the other: $ d = 7 - a $, making substitution simpler in larger equations.
- Foundation for Systems: This form is helpful in solving systems of equations, modeling real-world problems, and optimizing under constraints.
- Enhanced Readability: Cleaner equations are easier to interpret and validate, reducing errors in complex problem-solving.
