Subtract $ 75h $ and $ 200 $ from both sides: - Feedz API
Understanding How to Subtract $75h + 200$ from Both Sides: A Step-by-Step Guide for Algebra
Understanding How to Subtract $75h + 200$ from Both Sides: A Step-by-Step Guide for Algebra
When solving equations in algebra, a common technique is isolating the variable by moving constants to one side of the equation. One foundational but often overlooked step is subtracting $75h + 200$ from both sides of an equation. This approach simplifies complex expressions and strengthens your understanding of equation balancing.
In this article, we’ll explore what it means to subtract $75h + 200$ from both sides of an equation, why this step matters, and how doing so helps maintain equality while simplifying expressions.
Understanding the Context
What Does It Mean to Subtract $75h + 200$ from Both Sides?
At its core, subtracting $75h + 200$ from both sides of an equation ensures that the equation remains balanced. The principle follows from the addition-preservation rule — whatever you do to one side, you must do to the other.
For example, consider the equation:
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Key Insights
$$
x + 75h + 200 = 5h + 500
$$
If we subtract $75h + 200$ from both sides, we get:
$$
x + 75h + 200 - (75h + 200) = (5h + 500) - (75h + 200)
$$
On the left, the $+75h + 200$ cancels out, leaving just $x$. On the right, we simplify further:
$$
x = 5h + 500 - 75h - 200
$$
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📰 \boxed{\dfrac{80}{243}} 📰 Question: A linguist analyzes a hypothetical language where each word is 4 phonemes long, each phoneme independently from a set of 5. What is the probability that a randomly chosen word has exactly 2 distinct phonemes? 📰 Solution: First, choose 2 phonemes from 5: $ \binom{5}{2} = 10 $. For each pair, the number of 4-phoneme words using both phonemes (but not just one) is $ 2^4 - 2 = 14 $ (subtracting the two monochromatic words). Total favorable outcomes: $ 10 \cdot 14 = 140 $. Total possible words: $ 5^4 = 625 $. Probability:Final Thoughts
Now combine like terms:
$$
x = (-70h) + 300
$$
Why Subtract $75h + 200$ from Both Sides?
This transformation serves multiple purposes:
- Isolates the variable — Helping move all constants to one side simplifies finding the value of $h$ or $x$.
- Balances the equation — Maintains mathematical integrity by preserving equality.
- Simplifies further steps — Enables easier combination of like terms, making equations easier to solve.
This method is particularly useful in more complex equations involving multiple variables like $h$ or $x$, where immediate isolation of the variable isn’t straightforward.
Real-World Analogy
Think of an equation like a seesaw: both sides must always balance. If you remove the same weight ($75h + 200$) from each side, the perspective (the equation) remains unchanged while revealing new clarity — perhaps exposing the path to the unknown variable.
