$ (37a + 7b + c) - (19a + 5b + c) = -12 - 6 $

Simplifying the Equation: $ (37a + 7b + c) - (19a + 5b + c) = -12 - 6 $

Understanding algebraic expressions can sometimes feel complex, but breaking down equations step-by-step makes them far more manageable. Today, we’ll explore the equation $ (37a + 7b + c) - (19a + 5b + c) = -12 - 6 $ and simplify it intelligently.

Understanding the Context

Step 1: Rewrite the subtraction as distribution

The left-hand side involves subtraction of two binomials. Distribute the negative sign across the second group:

$$
(37a + 7b + c) - 19a - 5b - c
$$

Now combine like terms:

Solved 17) 6a + b + c = 8 -6a + b + c = -20 -3a + 4b - 3c = | Chegg.com

Image Gallery

Solved c) 3A+4B+5C+6D2B+A+4D+3C2C−A8D+6C−A+4B=7=5=3=1 d) | Chegg.com

Solved Is the set S = {(7a -5b + c,a -b + c,c-a, b + c,a, b | Chegg.com

Solved: a) 4a+7b+5a-b b) 6c+4d-c-7d [Math]

Key Insights

For $ a $: $ 37a - 19a = 18a $
For $ b $: $ 7b - 5b = 2b $
For $ c $: $ c - c = 0 $

So the simplified left side becomes:
$$
18a + 2b
$$

Step 2: Simplify the right-hand side

The right-hand side is a constant expression:

🔗 Related Articles You Might Like:

📰 mythology 📰 the outsiders 📰 civil rights movement 📰 How A Penny Worth Only A Cent Made Over 10 Millionshocking Story You Wont Stop Reading 7814175 📰 Youll Never Believe Its Top Hookup Appclick To Unlock Hidden Matches 9781005 📰 Note 9 Screen Color Issue 9019119 📰 The Untold Truth Behind Skyrims Mysterious Skyline Legends 8120887 📰 The Shocking Conversions You Wont Believe Are Possible 8610229 📰 Time For Second Part Frac20080 25 Hours 1304048 📰 Never Thought Purdue Would Use My Name In The Scandal That Shook Campus 6500380 📰 Youre Missing Outheres How Fidelity Investments Check Can Boost Your Portfolio Today 5228120 📰 Aqms Stock Surges Is It The Missing Piece In Your Profitable Portfolio 9384348 📰 Skin Dryness In Newborn 8696831 📰 Opposite Meaning Of Benefit 9640714 📰 Torrid Credit Card 4056291 📰 Hive Stock 778809 📰 The Hottest Trade Alert Arx Stock Surpose Will It Be The Next Billion Dollar Hit 7275683 📰 You Wont Believe Whats Truly Special In Birmingham Almade By The People Who Know Its Soul 992332

Final Thoughts

$$
-12 - 6 = -18
$$

So now the equation looks like:
$$
18a + 2b = -18
$$

Step 3: Simplify further

We can factor the left-hand side by pulling out the common factor 2:

$$
2(9a + b) = -18
$$

Divide both sides by 2:
$$
9a + b = -9
$$

What does the simplified equation mean?

We’ve transformed:
$$
(37a + 7b + c) - (19a + 5b + c) = -12 - 6
$$
into:
$$
9a + b = -9
$$