Unlocking the Mystery: 3n + 5 = 2n
Have you ever come across an equation like 3n + 5 = 2n and wondered how to solve it? You're not alone! This type of equation, where we're trying to find the value of an unknown variable (in this case, 'n'), pops up frequently in algebra.
Let's break down how to solve this equation, using insights from the popular Q&A platform Brainly.
Understanding the Equation
The equation 3n + 5 = 2n represents a balance. Think of it like a scale with weights on both sides. To find the value of 'n' that makes the equation true, we need to make sure both sides of the scale weigh the same.
StepbyStep Solution

Isolate 'n': Our goal is to get all the 'n' terms on one side of the equation. To do this, we can subtract 2n from both sides. This gives us:
3n + 5  2n = 2n  2n
This simplifies to:
n + 5 = 0

Solve for 'n': Now we need to isolate 'n'. We can do this by subtracting 5 from both sides:
n + 5  5 = 0  5
This simplifies to:
n = 5
Therefore, the solution to the equation 3n + 5 = 2n is n = 5.
Brainly Insights:

User 'mathlover' on Brainly: "You can think of it like moving the 'n' terms to one side of the equation and the constant terms to the other side." This is a great way to visualize the process of solving the equation.

User 'algebraexpert' on Brainly: "Remember that whatever you do to one side of the equation, you must also do to the other side." This emphasizes the importance of keeping the equation balanced throughout the solution process.
Additional Explanations:

Why do we subtract 2n? We subtract 2n because it's the 'n' term on the right side of the equation. This ensures that we have all the 'n' terms together on the left side.

How can I check my answer? To check your answer, substitute n = 5 back into the original equation:
3(5) + 5 = 2(5)
15 + 5 = 10
10 = 10
Since both sides of the equation are equal, our solution is correct.
RealWorld Examples:
Equations like 3n + 5 = 2n are used in various realworld applications:
 Finance: Calculating interest earned on savings or debt.
 Engineering: Determining the load capacity of structures.
 Economics: Modeling the supply and demand of goods.
In Conclusion
Solving equations like 3n + 5 = 2n is a fundamental skill in algebra. By applying basic algebraic operations and keeping the equation balanced, we can efficiently find the value of the unknown variable. As we have seen, these equations have practical applications in various fields, making the ability to solve them essential for understanding the world around us.