Understanding the Algebraic Equation: ⇝ 100 = 58 + 2mn ⇝ 2mn = 42 ⇝ mn = 21

Mathematics is not just about solving equations—it’s a powerful tool that helps simplify real-world problems, logical puzzles, and even data analysis. Today, we break down a classic algebraic expression:
100 = 58 + 2mn, and explore how it leads to mn = 21 through clear step-by-step reasoning.

Understanding the Context

Step 1: Start with the Given Equation

We begin with the equation:
100 = 58 + 2mn
This equation sets a total value (100) equal to a known quantity (58) plus a term involving two variables, 2mn.

Step 2: Isolate the Term with Variables

To solve for mn, subtract 58 from both sides:
100 – 58 = 2mn
42 = 2mn

This simplifies the problem by removing the constant on one side:
2mn = 42

\Rightarrow 100 = 58 + 2mn \Rightarrow 2mn = 42 \Rightarrow mn = 21

Key Insights

Step 3: Solve for mn

Now divide both sides by 2 to isolate mn:
mn = 42 ÷ 2
mn = 21

Why This Matters: Applications in Math and Beyond

This simple algebraic manipulation is foundational in many fields, including:

  • Algebraic reasoning: Teaching students how to isolate variables and solve equations.
  • Problem solving: Breaking down complex problems into manageable steps.
  • Data modeling: Expressing relationships between variables in scientific research or finance.

Continue Reading

If the function \(f(x) = 2x^2 - 3x + 1\), determine \(f(3)\).
Substitute \(x = 3\):
\[ f(3) = 2(3)^2 - 3(3) + 1 = 2 \times 9 - 9 + 1 = 18 - 9 + 1 = 10 \]

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Final Thoughts

Summary

Starting from 100 = 58 + 2mn, we derived that:

  1. 2mn = 42
  2. Finally, mn = 21

Understanding this process strengthens your algebraic thinking and empowers you to tackle a wide range of mathematical challenges.

Key Takeaways

  • Always isolate the variable term by performing inverse operations.
  • Step-by-step simplification builds confidence and accuracy.
  • This method illustrates the beauty of algebra in simplifying real-life equations.

Whether you're a student, teacher, or data enthusiast, mastering such equations helps unlock deeper mathematical insight and critical thinking skills.
Happy solving!

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