0.05x + 800 - 0.08x = 680

February 17, 2026

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.

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.

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.

Step 2: Isolate the Variable Term

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

Why This Equation Matters: Real-World Applications

Equations like 0.05x + 800 − 0.08x = 680 model scenarios where two opposing trends balance out. For example:- Business: Calculating break-even points where costs (800) and variable expenses (0.08x per unit) minus revenue (0.05x per unit) equals a net target (680).- Finance: Adjusting investment balances when fixed deposits (800) minus interest (0.08x) minus withdrawals (0.05x) match a desired amount (680).- Science: Modeling reaction rates or temperature changes where opposing factors sum to a target value.

Summary: Quick Recap

Combine like terms:0.05x − 0.08x + 800 = 680 → −0.03x + 800 = 680
Isolate x-term:−0.03x = −120
Solve:x = −120 ÷ (−0.03) = 4000

Final Thoughts

Mastering the solution of equations like 0.05x + 800 - 0.08x = 680 builds essential algebra skills. From simplifying expressions and isolating variables to applying these techniques in real-life problem-solving, each step strengthens your mathematical foundation. Keep practicing—algebra is a powerful tool for understanding the world!

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