\[ (19a + 5b + c) - (7a + 3b + c) = 25 - 11 \] - inBeat
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:
📰 paypal atm card 📰 site of the protein synthesis 📰 beloved pdf 📰 5Hookup Removed From Hrts Black Box Label The Drug Industry Is Breaking News 3672920 📰 Characters In Borderlands 4 3024604 📰 Rome 2 Game 5424792 📰 G E O M 4374225 📰 Bruce Bolts Gloves Are Every Players Game Changer You Never Knew You Needed 1425460 📰 Chatgpt Plus Subscribers 4379310 📰 Rapbeh Reveals The Shocking Truth About His Hidden Past 4940792 📰 Breakthrough Alert Litecoin Etf Surpasses Expectations Heres Whats Actually Happening 710050 📰 Corrected What Is The Observed Biomass Per Fish 6805090 📰 Clbtw Stock Is Rising Fastwhat Every Trader Should Know Now 7876323 📰 Business Rewards Credit Card 4796363 📰 God Bless And 1711481 📰 Game Dvr 2876908 📰 Sonoma Colleges 2555837 📰 Eq 1 Indicating That Fx Is A Decreasing Function On Its Domain Thus Fx Does Not Have A Maximum In The Traditional Sense But Decreases Towards Infty As X O 1 And Increases Without Bound As X O Infty Therefore There Is No Finite X That Maximizes Fx 1943458Final 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
