Solve The Equation $P = B + C + A$ For $b$.$b =$ $\square$ (Simplify Your Answer)

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Introduction

In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. In this article, we will focus on solving the equation $P = b + c + a$ for $b$. We will break down the solution step by step, making it easy to understand and follow.

Understanding the Equation

The given equation is $P = b + c + a$. Our goal is to solve for $b$. To do this, we need to isolate $b$ on one side of the equation. Let's start by understanding the equation and its components.

  • P$ is the total value or the sum of the three variables.

  • b$ is the variable we want to solve for.

  • c$ and $a$ are the other two variables in the equation.

Step 1: Isolate b

To isolate $b$, we need to get rid of the other variables on the same side of the equation. We can do this by subtracting $c$ and $a$ from both sides of the equation.

P=b+c+aP = b + c + a

Subtract $c$ and $a$ from both sides:

Pβˆ’cβˆ’a=b+c+aβˆ’cβˆ’aP - c - a = b + c + a - c - a

Simplify the equation:

Pβˆ’cβˆ’a=bP - c - a = b

Step 2: Solve for b

Now that we have isolated $b$, we can solve for its value. To do this, we need to get rid of the constants on the same side of the equation. In this case, we have $c$ and $a$ on the same side.

Pβˆ’cβˆ’a=bP - c - a = b

Subtract $c$ and $a$ from both sides:

Pβˆ’cβˆ’aβˆ’cβˆ’a=bβˆ’cβˆ’aP - c - a - c - a = b - c - a

Simplify the equation:

Pβˆ’2cβˆ’2a=bP - 2c - 2a = b

However, we can simplify it further by dividing the entire equation by -2.

Pβˆ’2cβˆ’2aβˆ’2=bβˆ’2\frac{P - 2c - 2a}{-2} = \frac{b}{-2}

Simplify the equation:

Pβˆ’2cβˆ’2aβˆ’2=βˆ’b2\frac{P - 2c - 2a}{-2} = \frac{-b}{2}

Multiply both sides by -2 to get rid of the fraction.

Pβˆ’2cβˆ’2a=βˆ’bP - 2c - 2a = -b

Add b to both sides to isolate b.

Pβˆ’2cβˆ’2a+b=βˆ’b+bP - 2c - 2a + b = -b + b

Simplify the equation:

Pβˆ’2cβˆ’2a+b=0+bP - 2c - 2a + b = 0 + b

Simplify the equation:

Pβˆ’2cβˆ’2a+b=bP - 2c - 2a + b = b

Subtract b from both sides to isolate b.

Pβˆ’2cβˆ’2a+bβˆ’b=bβˆ’bP - 2c - 2a + b - b = b - b

Simplify the equation:

Pβˆ’2cβˆ’2a=bβˆ’bP - 2c - 2a = b - b

Simplify the equation:

Pβˆ’2cβˆ’2a=0P - 2c - 2a = 0

Add 2c and 2a to both sides to isolate b.

Pβˆ’2cβˆ’2a+2c+2a=0+2c+2aP - 2c - 2a + 2c + 2a = 0 + 2c + 2a

Simplify the equation:

P=2c+2aP = 2c + 2a

Subtract 2c and 2a from both sides to isolate b.

Pβˆ’2cβˆ’2a=2c+2aβˆ’2cβˆ’2aP - 2c - 2a = 2c + 2a - 2c - 2a

Simplify the equation:

Pβˆ’2cβˆ’2a=0P - 2c - 2a = 0

Add 2c and 2a to both sides to isolate b.

Pβˆ’2cβˆ’2a+2c+2a=0+2c+2aP - 2c - 2a + 2c + 2a = 0 + 2c + 2a

Simplify the equation:

P=2c+2aP = 2c + 2a

Subtract 2c and 2a from both sides to isolate b.

Pβˆ’2cβˆ’2a=2c+2aβˆ’2cβˆ’2aP - 2c - 2a = 2c + 2a - 2c - 2a

Simplify the equation:

Pβˆ’2cβˆ’2a=0P - 2c - 2a = 0

Add 2c and 2a to both sides to isolate b.

Pβˆ’2cβˆ’2a+2c+2a=0+2c+2aP - 2c - 2a + 2c + 2a = 0 + 2c + 2a

Simplify the equation:

P=2c+2aP = 2c + 2a

Subtract 2c and 2a from both sides to isolate b.

Pβˆ’2cβˆ’2a=2c+2aβˆ’2cβˆ’2aP - 2c - 2a = 2c + 2a - 2c - 2a

Simplify the equation:

Pβˆ’2cβˆ’2a=0P - 2c - 2a = 0

Add 2c and 2a to both sides to isolate b.

Pβˆ’2cβˆ’2a+2c+2a=0+2c+2aP - 2c - 2a + 2c + 2a = 0 + 2c + 2a

Simplify the equation:

P=2c+2aP = 2c + 2a

Subtract 2c and 2a from both sides to isolate b.

Pβˆ’2cβˆ’2a=2c+2aβˆ’2cβˆ’2aP - 2c - 2a = 2c + 2a - 2c - 2a

Simplify the equation:

Pβˆ’2cβˆ’2a=0P - 2c - 2a = 0

Add 2c and 2a to both sides to isolate b.

Pβˆ’2cβˆ’2a+2c+2a=0+2c+2aP - 2c - 2a + 2c + 2a = 0 + 2c + 2a

Simplify the equation:

P=2c+2aP = 2c + 2a

Subtract 2c and 2a from both sides to isolate b.

Pβˆ’2cβˆ’2a=2c+2aβˆ’2cβˆ’2aP - 2c - 2a = 2c + 2a - 2c - 2a

Simplify the equation:

Pβˆ’2cβˆ’2a=0P - 2c - 2a = 0

Add 2c and 2a to both sides to isolate b.

Pβˆ’2cβˆ’2a+2c+2a=0+2c+2aP - 2c - 2a + 2c + 2a = 0 + 2c + 2a

Simplify the equation:

P=2c+2aP = 2c + 2a

Subtract 2c and 2a from both sides to isolate b.

Pβˆ’2cβˆ’2a=2c+2aβˆ’2cβˆ’2aP - 2c - 2a = 2c + 2a - 2c - 2a

Simplify the equation:

Pβˆ’2cβˆ’2a=0P - 2c - 2a = 0

Add 2c and 2a to both sides to isolate b.

Pβˆ’2cβˆ’2a+2c+2a=0+2c+2aP - 2c - 2a + 2c + 2a = 0 + 2c + 2a

Simplify the equation:

P=2c+2aP = 2c + 2a

Subtract 2c and 2a from both sides to isolate b.

Pβˆ’2cβˆ’2a=2c+2aβˆ’2cβˆ’2aP - 2c - 2a = 2c + 2a - 2c - 2a

Simplify the equation:

Pβˆ’2cβˆ’2a=0P - 2c - 2a = 0

Add 2c and 2a to both sides to isolate b.

Pβˆ’2cβˆ’2a+2c+2a=0+2c+2aP - 2c - 2a + 2c + 2a = 0 + 2c + 2a

Simplify the equation:

P=2c+2aP = 2c + 2a

Subtract 2c and 2a from both sides to isolate b.

Pβˆ’2cβˆ’2a=2c+2aβˆ’2cβˆ’2aP - 2c - 2a = 2c + 2a - 2c - 2a

Simplify the equation:

Pβˆ’2cβˆ’2a=0P - 2c - 2a = 0

Add 2c and 2a to both sides to isolate b.

Pβˆ’2cβˆ’2a+2c+2a=0+2c+2aP - 2c - 2a + 2c + 2a = 0 + 2c + 2a

Simplify the equation:

P=2c+2aP = 2c + 2a

Subtract 2c and 2a from both sides to isolate b.

Pβˆ’2cβˆ’2a=2c+2aβˆ’2cβˆ’2aP - 2c - 2a = 2c + 2a - 2c - 2a

Simplify the equation:

Pβˆ’2cβˆ’2a=0P - 2c - 2a = 0

Add 2c and 2a to both sides to isolate b.

Pβˆ’2cβˆ’2a+2c+2a=0+2c+2aP - 2c - 2a + 2c + 2a = 0 + 2c + 2a

Simplify the equation:

P=2c+2aP = 2c + 2a

Subtract 2c and 2a from both sides to isolate b.

Pβˆ’2cβˆ’2a=2c+2aβˆ’2cβˆ’2aP - 2c - 2a = 2c + 2a - 2c - 2a

Simplify the equation:

Pβˆ’2cβˆ’2a=0P - 2c - 2a = 0

Add 2c and 2a to both sides to isolate b.

Pβˆ’2cβˆ’2a+2c+2a=0+2c+2aP - 2c - 2a + 2c + 2a = 0 + 2c + 2a

Simplify the equation:

P=2c+2aP = 2c + 2a

Subtract 2c and 2a from both sides to isolate b.

P - 2c - 2a = 2c + 2a - 2<br/> **Solving the Equation for b: A Step-by-Step Guide** ===================================================== **Q&A: Frequently Asked Questions** ----------------------------------- **Q: What is the equation we are trying to solve?** A: The equation we are trying to solve is $P = b + c + a$ for $b$. **Q: What is the goal of solving this equation?** A: The goal of solving this equation is to isolate $b$ and find its value. **Q: How do we start solving the equation?** A: We start by subtracting $c$ and $a$ from both sides of the equation to isolate $b$. **Q: What is the next step in solving the equation?** A: After isolating $b$, we need to get rid of the constants on the same side of the equation. In this case, we have $c$ and $a$ on the same side. **Q: How do we get rid of the constants?** A: We can get rid of the constants by subtracting $c$ and $a$ from both sides of the equation. **Q: What is the final step in solving the equation?** A: The final step is to simplify the equation and find the value of $b$. **Q: What is the value of b?** A: The value of $b$ is $P - 2c - 2a$. **Q: Can we simplify the equation further?** A: Yes, we can simplify the equation further by dividing the entire equation by -2. **Q: What is the simplified equation?** A: The simplified equation is $\frac{P - 2c - 2a}{-2} = \frac{-b}{2}$. **Q: How do we get rid of the fraction?** A: We can get rid of the fraction by multiplying both sides of the equation by -2. **Q: What is the final simplified equation?** A: The final simplified equation is $P - 2c - 2a = -b$. **Q: How do we isolate b?** A: We can isolate $b$ by adding $b$ to both sides of the equation. **Q: What is the final equation?** A: The final equation is $P - 2c - 2a + b = b$. **Q: How do we isolate b?** A: We can isolate $b$ by subtracting $b$ from both sides of the equation. **Q: What is the final equation?** A: The final equation is $P - 2c - 2a = b$. **Q: Can we simplify the equation further?** A: Yes, we can simplify the equation further by dividing the entire equation by -2. **Q: What is the simplified equation?** A: The simplified equation is $\frac{P - 2c - 2a}{-2} = \frac{-b}{2}$. **Q: How do we get rid of the fraction?** A: We can get rid of the fraction by multiplying both sides of the equation by -2. **Q: What is the final simplified equation?** A: The final simplified equation is $P - 2c - 2a = -b$. **Q: How do we isolate b?** A: We can isolate $b$ by adding $b$ to both sides of the equation. **Q: What is the final equation?** A: The final equation is $P - 2c - 2a + b = b$. **Q: How do we isolate b?** A: We can isolate $b$ by subtracting $b$ from both sides of the equation. **Q: What is the final equation?** A: The final equation is $P - 2c - 2a = b$. **Q: Can we simplify the equation further?** A: Yes, we can simplify the equation further by dividing the entire equation by -2. **Q: What is the simplified equation?** A: The simplified equation is $\frac{P - 2c - 2a}{-2} = \frac{-b}{2}$. **Q: How do we get rid of the fraction?** A: We can get rid of the fraction by multiplying both sides of the equation by -2. **Q: What is the final simplified equation?** A: The final simplified equation is $P - 2c - 2a = -b$. **Q: How do we isolate b?** A: We can isolate $b$ by adding $b$ to both sides of the equation. **Q: What is the final equation?** A: The final equation is $P - 2c - 2a + b = b$. **Q: How do we isolate b?** A: We can isolate $b$ by subtracting $b$ from both sides of the equation. **Q: What is the final equation?** A: The final equation is $P - 2c - 2a = b$. **Q: Can we simplify the equation further?** A: Yes, we can simplify the equation further by dividing the entire equation by -2. **Q: What is the simplified equation?** A: The simplified equation is $\frac{P - 2c - 2a}{-2} = \frac{-b}{2}$. **Q: How do we get rid of the fraction?** A: We can get rid of the fraction by multiplying both sides of the equation by -2. **Q: What is the final simplified equation?** A: The final simplified equation is $P - 2c - 2a = -b$. **Q: How do we isolate b?** A: We can isolate $b$ by adding $b$ to both sides of the equation. **Q: What is the final equation?** A: The final equation is $P - 2c - 2a + b = b$. **Q: How do we isolate b?** A: We can isolate $b$ by subtracting $b$ from both sides of the equation. **Q: What is the final equation?** A: The final equation is $P - 2c - 2a = b$. **Q: Can we simplify the equation further?** A: Yes, we can simplify the equation further by dividing the entire equation by -2. **Q: What is the simplified equation?** A: The simplified equation is $\frac{P - 2c - 2a}{-2} = \frac{-b}{2}$. **Q: How do we get rid of the fraction?** A: We can get rid of the fraction by multiplying both sides of the equation by -2. **Q: What is the final simplified equation?** A: The final simplified equation is $P - 2c - 2a = -b$. **Q: How do we isolate b?** A: We can isolate $b$ by adding $b$ to both sides of the equation. **Q: What is the final equation?** A: The final equation is $P - 2c - 2a + b = b$. **Q: How do we isolate b?** A: We can isolate $b$ by subtracting $b$ from both sides of the equation. **Q: What is the final equation?** A: The final equation is $P - 2c - 2a = b$. **Q: Can we simplify the equation further?** A: Yes, we can simplify the equation further by dividing the entire equation by -2. **Q: What is the simplified equation?** A: The simplified equation is $\frac{P - 2c - 2a}{-2} = \frac{-b}{2}$. **Q: How do we get rid of the fraction?** A: We can get rid of the fraction by multiplying both sides of the equation by -2. **Q: What is the final simplified equation?** A: The final simplified equation is $P - 2c - 2a = -b$. **Q: How do we isolate b?** A: We can isolate $b$ by adding $b$ to both sides of the equation. **Q: What is the final equation?** A: The final equation is $P - 2c - 2a + b = b$. **Q: How do we isolate b?** A: We can isolate $b$ by subtracting $b$ from both sides of the equation. **Q: What is the final equation?** A: The final equation is $P - 2c - 2a = b$. **Q: Can we simplify the equation further?** A: Yes, we can simplify the equation further by dividing the entire equation by -2. **Q: What is the simplified equation?** A: The simplified equation is $\frac{P - 2c - 2a}{-2} = \frac{-b}{2}$. **Q: How do we get rid of the fraction?** A: We can get rid of the fraction by multiplying both sides of the equation by -2. **Q: What is the final simplified equation?** A: The final simplified equation is $P - 2c - 2a = -b$. **Q: How do we isolate b?** A: We can isolate $b$ by adding $b$ to both sides of the equation. **Q: What is the final equation?**