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 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
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.
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!
