Subtract $ 75h $ and $ 200 $ from both sides:

February 22, 2026

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.

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:

$$ x + 75h + 200 = 5h + 500 $$

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:

$$ x = 5h + 500 - 75h - 200 $$

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.

Step-by-Step Example

Let’s walk through solving:

$$ 3h + 75h + 200 = 400 $$

Step 1: Combine like terms on the left:

$$ 78h + 200 = 400 $$

Step 2: Subtract $200$ from both sides:

$$ 78h + 200 - 200 = 400 - 200 $$

$$ 78h = 200 $$

Step 3: Now solve for $h$ by dividing both sides (note: this uses subtraction as foundational):

$$ h = rac{200}{78} = rac{100}{39} $$

Key Takeaways

Subtracting a sum like $75h + 200$ from both sides removes constants from one side, aiding variable isolation.
The key principle is maintaining balance — operations applied to one side must be mirrored on the other.
This technique lays the groundwork for solving multi-step equations common in advanced algebra.

Conclusion

Subtracting $75h + 200$ from both sides is more than a mechanical step — it’s a fundamental strategy in algebraic problem-solving. Mastering this builds confidence in manipulating equations and solves one of the first hurdles in moving from basic to complex algebraic reasoning. Keep practicing, and watch how small but deliberate steps transform confusing equations into clear solutions!

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