How to Solve the Equation 0.05x + 800 - 0.08x = 680: A Step-by-Step Guide

Mathematics often presents challenges in seemingly simple equations, but solving linear expressions like 0.05x + 800 - 0.08x = 680 can become intuitive with the right approach. In this article, we’ll break down how to solve this equation step-by-step, understand its structure, and explore real-world applications. Whether you're a student learning algebra or someone brushing up on equations, this guide will help you master solving 0.05x + 800 - 0.08x = 680 efficiently.

Understanding the Context

The Equation at a Glance

Start with the equation:
0.05x + 800 - 0.08x = 680

On the left-hand side, combine like terms involving x, while treating the constant 800 as a standalone value. This helps simplify the equation and isolate x for solving.

Sample 7

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Sample 7
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Key Insights

Step 1: Combine Like Terms

Identify coefficients of x:
0.05x − 0.08x = (−0.08 + 0.05)x = −0.03x

So the equation becomes:
−0.03x + 800 = 680

This simplification reduces complexity and prepares the equation for the next step.

Continue Reading

Note that by the well-known inequality:
with equality if and only if $ a = b = c $. Therefore,
and also equals 3 when $ a = b = c $.

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Final Thoughts

Step 2: Isolate the Variable Term

To solve for x, first subtract 800 from both sides:
−0.03x + 800 − 800 = 680 − 800
Resulting in:
−0.03x = −120

Now the variable term is isolated with a negative coefficient—this is normal in algebra and won’t affect the final solution.

Step 3: Solve for x

Divide both sides by −0.03:
x = −120 ÷ (−0.03)
x = 4000

This positive solution makes sense, especially in contextual problems like financial balancing or measurements.

Final Answer

✅ x = 4000