+ 10e = 150 + 7e

Solving the Equation: +10e = 150 + 7e – A Step-by-Step Explanation

Understanding how to solve linear equations involving exponential terms can boost your math skills and deepen your grasp of algebra. In this article, we’ll explore the equation +10e = 150 + 7e and break down how to solve it step-by-step—ideal for students, educators, and math enthusiasts looking to strengthen their equation-solving abilities.

Understanding the Context

Understanding the Equation

The given equation is:
10e = 150 + 7e
Here, e represents the base of the natural logarithm (approximately equal to 2.718), though in algebra problems like this one, e is typically used as a variable to solve for rather than a constant.

Step 1: Isolate Terms Involving e

To solve for e, begin by gathering all exponential terms on one side of the equation and the constant terms on the other. Subtract 7e from both sides:
10e – 7e = 150

This simplifies to:
3e = 150

Key Insights

Step 2: Solve for e

Now divide both sides by 3:
e = 150 / 3
e = 50

Verification

Plug e = 50 back into the original equation to check:
Left side: 10e = 10 × 50 = 500
Right side: 150 + 7e = 150 + 7 × 50 = 150 + 350 = 500

Both sides equal 500, confirming the solution is correct.

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Final Thoughts

Why This Equation Matters

While exponential variables like e often appear in advanced calculus and calculus-based problems (e.g., exponential growth, decay), simpler versions like 10e = 150 + 7e help learners practice algebraic manipulation and isolate unknowns. Mastering these techniques prepares students for more complex scientific modeling and problem-solving tasks.

Tips for Solving Similar Equations

Always move all terms involving the variable to one side.
Combine constant terms on the opposite side.
Divide evenly to isolate the variable.
Always verify your solution by substituting back into the original equation.

Conclusion

The equation 10e = 150 + 7e simplifies neatly to yield e = 50—a straightforward example of algebraic reasoning that lays the foundation for tackling exponential equations in higher mathematics. Whether for homework, classwork, or personal practice, understanding how to solve for e enhances your analytical capabilities.

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Need more math help? Explore our guides on linear equations, logarithmic expressions, and exponential functions to sharpen your skills!