The realm of mathematics encompasses a vast array of equations, each with its own unique significance and complexity. Among these, the equation 6p=7p+10 holds a prominent position, intriguing minds with its simplicity yet profound implications. This equation invites us on an intellectual journey to unravel its meaning and discover the hidden truths it contains.

At first glance, 6p=7p+10 may appear deceptively simple, a mere string of algebraic symbols. However, upon closer examination, we uncover a deeper layer of complexity that requires careful analysis and a systematic approach to solve. As we embark on this mathematical expedition, let us explore the equation’s significance, its applications, and the insights it provides into the fascinating world of mathematics.

Throughout this article, we will delve into the various aspects of 6p=7p+10, unraveling its intricacies and revealing its true nature. We will explore different methods to solve this equation, examining its implications in various fields, and uncovering the underlying mathematical principles that govern its behavior. Prepare yourself for an enlightening journey as we embark on a comprehensive exploration of 6p=7p+10.

## Simplifying the Equation

To solve 6p=7p+10, we must first simplify the equation by isolating the variable term (p) on one side and the constant term (10) on the other. This process involves subtracting 7p from both sides of the equation:

6p – 7p = 7p + 10 – 7p

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Simplifying further, we obtain:

-p = 10

## Solving for p

To solve for p, we divide both sides of the equation by -1, which effectively cancels out the negative sign and isolates p:

(-p)/(-1) = 10/(-1)

Simplifying, we find:

p = -10

## Checking the Solution

To verify whether our solution is correct, we substitute p = -10 back into the original equation:

6(-10) = 7(-10) + 10

-60 = -70 + 10

-60 = -60

Since both sides of the equation are equal, we can conclude that p = -10 is the correct solution.

## Applications of the Equation

The equation 6p=7p+10 has practical applications in various fields, including:

1. **Economics:** In economics, the equation can be used to model scenarios such as supply and demand, price elasticity, and consumer behavior.

2. **Engineering:** In engineering, the equation can be used to analyze and design systems, determine forces and stresses, and optimize performance.

3. **Finance:** In finance, the equation can be used to calculate interest rates, determine loan payments, and assess investment strategies.

## Underlying Mathematical Principles

The equation 6p=7p+10 is governed by the following mathematical principles:

1. **Equality of Equations:** The equation represents a statement of equality, indicating that the expression on the left-hand side (LHS) is equal to the expression on the right-hand side (RHS).

2. **Algebraic Operations:** The equation involves algebraic operations such as addition, subtraction, and multiplication. Understanding these operations is crucial for solving the equation.

3. **Isolating Variables:** To solve for the variable (p), we must isolate it on one side of the equation by performing algebraic operations.

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