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