How to Solve 240 = 6 × w × 5: A Step-by-Step Explanation

Mathematics often involves breaking down equations to uncover simple, clear solutions. One such problem—240 = 6 × w × 5—may seem complicated at first glance, but with a few straightforward steps, you can easily find that w = 8. In this article, we’ll walk through how to solve this equation confidently, understand its structure, and explore practical ways to approach similar algebraic problems.

Breaking Down the Equation

Understanding the Context

At first, the equation 240 = 6 × w × 5 looks like a sudden leap, but grouping the constants transforms it into a manageable form:

240 = 6 × 5 × w

By multiplying 6 and 5 first, we simplify the right-hand side:

240 = 30w

240 = 6 × w × 5 → 240 = 30w → w = 240 / 30 = 8

Key Insights

Now the equation clearly shows that 30 times w equals 240. This format makes it much easier to isolate w.

Isolating the Variable w

To solve for w, we need to divide both sides of the equation by 30:

240 ÷ 30 = w

This operation reverses multiplication, allowing us to express w independently:

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Wir müssen überprüfen, ob alle Wurzeln \( w_i \) reell und positiv sind, da nur reelle positive \( w_i \) zu reellen \( v = w_i^2 \) führen. Wir analysieren das kubische Polynom \( f(w) = w^3 - 8w^2 + 9w - 18 \). Berechne Extremstellen:
\( f'(w) = 3w^2 - 16w + 9 \). Diskriminante: \( 256 - 108 = 148 > 0 \), zwei kritische Punkte:
\( w = \frac{16 \pm \sqrt{148}}{6} = \frac{16 \pm 2\sqrt{37}}{6} = \frac{8 \pm \sqrt{37}}{3} \).

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Final Thoughts

w = 240 / 30

w = 8

Now w is clearly defined as 8, confirming the solution with simple division.

Why This Simplification Matters

Understanding how to simplify multi-factor equations like 240 = 6 × w × 5 is valuable for o rder of operations skills. Instead of facing a confusing multiplication first, grouping constants first streamlines the process—turning tricky expressions into linear equations.

Practice with a Similar Problem

Want to test your understanding? Try solving:
180 = 9 × w × 2

Simplify first:
180 = 18w
Then divide:
w = 180 ÷ 18 = 10

This kind of algebraic thinking builds confidence in handling variables across math, physics, and everyday problem-solving.

Final Thoughts