Solving the Equation 75x = 50x + 2000: A Step-by-Step Guide

If you're learning algebra or brushing up on equation-solving skills, the equation 75x = 50x + 2000 is a great example of linear equations that help build foundational math understanding. In this article, we’ll walk through how to solve this equation, explain the logic behind each step, and explore its real-world applications.

Understanding the Context

What Is the Equation?

We are solving for x in the equation:

75x = 50x + 2000

This is a linear equation with one variable. Solving such equations helps you isolate the variable and find its exact value—skills essential in math, engineering, economics, and many other fields.

75x = 50x + 2000

Key Insights

Step-by-Step Solution

Step 1: Eliminate the variable from one side
Start by subtracting 50x from both sides to gather all x-terms on the left:

75x - 50x = 50x + 2000 - 50x
25x = 2000

Step 2: Solve for x
Now divide both sides by 25:

Continue Reading

Difference = 840,000 – 360,000 = 480,000
An epidemiologist estimates that 60% of a city’s population is susceptible to a new virus, and the infection rate is 0.3 per infected person per day. If there are 1,000 initially infected individuals, and each day each infected person transmits to 0.3 susceptible people on average, how many new infections occur in the first day?
Susceptible = 60% of 500,000 = 300,000

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Final Thoughts

x = 2000 ÷ 25
x = 80

Final Answer

The solution to the equation 75x = 50x + 2000 is:

x = 80

Why This Equation Matters

Understanding how to solve linear equations like this is key for:

  • Real-world modeling: Calculating break-even points, predicting costs, or analyzing earning trends.
  • Scientific and engineering applications: Setting up models where relationships grow proportionally.
  • Gaining problem-solving confidence: Each solved equation strengthens logical reasoning.