\[ (19a + 5b + c) - (7a + 3b + c) = 25 - 11 \] - IQnection
Title: Simplify and Solve: Solving the Equation (19a + 5b + c) − (7a + 3b + c) = 14
Title: Simplify and Solve: Solving the Equation (19a + 5b + c) − (7a + 3b + c) = 14
Introduction
Mastering algebraic equations is essential for students, educators, and anyone working with patterns and variables. One common type of problem involves simplifying expressions before solving. In this SEO-optimized guide, we explore the equation:
Understanding the Context
(19a + 5b + c) − (7a + 3b + c) = 25 − 11, and provide a step-by-step breakdown to solve it efficiently. With clear explanations, this article aims to help readers understand how to simplify complex expressions and arrive at accurate solutions—perfect for students preparing for algebra exams or anyone seeking clearer math comprehension.
Step-by-Step Breakdown of the Equation
Equation:
(19a + 5b + c) − (7a + 3b + c) = 25 − 11
Image Gallery
Key Insights
Step 1: Simplify the right-hand side
First, simplify the constant expression on the right:
25 − 11 = 14
So now the equation becomes:
(19a + 5b + c) − (7a + 3b + c) = 14
Step 2: Remove parentheses using the distributive property
When subtracting a parenthetical expression, distribute the negative sign:
= 19a + 5b + c − 7a − 3b − c
Step 3: Combine like terms
Group similar variables and constants:
(19a − 7a) + (5b − 3b) + (c − c)
= 12a + 2b + 0
= 12a + 2b
So now the equation simplifies to:
12a + 2b = 14
Step 4: Interpret the result
The equation has been reduced from involving three variables (a, b, c) to just two (a and b), meaning c cancels out completely—consistent with the original expression’s structure. This confirms the cancellation of c is valid and simplifies the solution pathway.
🔗 Related Articles You Might Like:
📰 Hellraiser Judgment Revealed: Horror at Its Most Twisted—Witness Reason to Run in Fear Right Now! 📰 You Won’t Believe What Happened When Hellraiser Cenobites Invaded Your Nightmares! 📰 Hellraiser Cenobites Unleashed: The Scariest Encounters You Must Watch Now! 📰 The Energy Shift Begins With Mega Starmiewatch The Magic Unfold Now 7094120 📰 Pizza Hut Personal Pizza 6534819 📰 Hades Game Story 329889 📰 The Card You Thought Was Lost Just Logged You Back Instrange Powerful Undeniable 7987028 📰 Justice Delayed Revealed Alameda County Superior Court Secrets Finally Out 2560810 📰 Windows 365 Enterprise The Secret Power Behind Seamless Workforce Cloud Computing 7642895 📰 Unleash The Future Of Payments With Myccpayyou Wont Believe Whats Inside 9233591 📰 Discover The Secret Tools Inside Peoplepc Webmail That Save Time Every Day 3483851 📰 The Clover Thats Craving Your Attention In Every Sunlit Corner 6719194 📰 Why Grlt Ihub Is Fueling Hollywoods Latest Obsessiondont Miss Out 1451638 📰 Best Business Accounts For Small Business 3407126 📰 Airpod Max 3394670 📰 Sarah Huckabee Net Worth 840512 📰 What Are Exchange Traded Funds 4218142 📰 Dollar Usd To Inr 5611610Final Thoughts
Step 5: Express the final simplified equation
We now have:
12a + 2b = 14
This can be further simplified by dividing through by 2 for a cleaner form:
6a + b = 7
Why This Equation Matters for Students and Learners
This problem exemplifies a powerful algebraic principle: simplifying expressions before solving. By reducing terms and eliminating redundant variables like c, learners:
- Improve their ability to approach complex equations confidently
- Develop skills in organizing terms systematically
- Enhance algebraic fluency, critical in higher math and STEM fields
Understanding how terms cancel and how coefficients simplify empowers students to tackle similar equations involving multiple variables and operations.
Final Solution & Key Takeaways
- Original Equation: (19a + 5b + c) − (7a + 3b + c) = 25 − 11
- Simplified Result: 12a + 2b = 14 → 6a + b = 7
- Variable c disappears due to cancellation—showing that not all terms require individual solving
- Purpose: Practice simplification and clarity in algebraic manipulation
