$ (37a + 7b + c) - (19a + 5b + c) = -12 - 6 $ - Crosslake
Simplifying the Equation: $ (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:
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:
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$$
-12 - 6 = -18
$$
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:
$$
9a + b = -9
$$
