Solve For R R R . R + 6 = − 5 R + 6 = -5 R + 6 = − 5 R = R = R =

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Introduction

Solving for a variable in an equation is a fundamental concept in mathematics, and it is essential to understand how to isolate the variable to find its value. In this article, we will focus on solving for the variable $r$ in the equation $r + 6 = -5$. This equation is a simple linear equation, and we will use basic algebraic techniques to solve for $r$.

Understanding the Equation

The given equation is $r + 6 = -5$. This equation states that the sum of $r$ and $6$ is equal to $-5$. To solve for $r$, we need to isolate the variable $r$ on one side of the equation.

Isolating the Variable

To isolate the variable $r$, we need to get rid of the constant term $6$ on the same side of the equation as $r$. We can do this by subtracting $6$ from both sides of the equation.

Subtracting 6 from Both Sides

When we subtract $6$ from both sides of the equation, we get:

$r + 6 - 6 = -5 - 6$

This simplifies to:

$r = -11$

Conclusion

In this article, we solved for the variable $r$ in the equation $r + 6 = -5$. We used basic algebraic techniques to isolate the variable $r$ on one side of the equation. By subtracting $6$ from both sides of the equation, we found that $r = -11$. This is the solution to the equation, and it represents the value of the variable $r$.

Step-by-Step Solution

Here is a step-by-step solution to the equation:

1. Start with the given equation: $r + 6 = -5$
2. Subtract $6$ from both sides of the equation: $r + 6 - 6 = -5 - 6$
3. Simplify the equation: $r = -11$

Example Use Case

Solving for a variable in an equation is a fundamental concept in mathematics, and it has many real-world applications. For example, in physics, we may need to solve for the velocity of an object given its acceleration and time. In finance, we may need to solve for the interest rate on a loan given the principal amount, time, and interest rate.

Tips and Tricks

Here are some tips and tricks to help you solve for a variable in an equation:

• Make sure to isolate the variable on one side of the equation.
• Use inverse operations to get rid of the constant term on the same side of the equation as the variable.
• Check your solution by plugging it back into the original equation.

Common Mistakes

Here are some common mistakes to avoid when solving for a variable in an equation:

• Not isolating the variable on one side of the equation.
• Not using inverse operations to get rid of the constant term on the same side of the equation as the variable.
• Not checking the solution by plugging it back into the original equation.

Conclusion

Solving for a variable in an equation is a fundamental concept in mathematics, and it is essential to understand how to isolate the variable to find its value. In this article, we solved for the variable $r$ in the equation $r + 6 = -5$. We used basic algebraic techniques to isolate the variable $r$ on one side of the equation. By subtracting $6$ from both sides of the equation, we found that $r = -11$. This is the solution to the equation, and it represents the value of the variable $r$.

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Introduction

In our previous article, we solved for the variable $r$ in the equation $r + 6 = -5$. We used basic algebraic techniques to isolate the variable $r$ on one side of the equation. In this article, we will answer some frequently asked questions about solving for a variable in an equation.

Q&A

Q: What is the first step in solving for a variable in an equation?

A: The first step in solving for a variable in an equation is to read and understand the equation. This includes identifying the variable and the constant term.

Q: How do I isolate the variable on one side of the equation?

A: To isolate the variable on one side of the equation, you need to get rid of the constant term on the same side of the equation as the variable. You can do this by using inverse operations, such as addition and subtraction.

Q: What is an inverse operation?

A: An inverse operation is a mathematical operation that undoes the effect of another operation. For example, addition and subtraction are inverse operations, as are multiplication and division.

Q: How do I use inverse operations to solve for a variable?

A: To use inverse operations to solve for a variable, you need to identify the operation that is being used to combine the variable and the constant term. Then, you need to use the inverse operation to isolate the variable.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable is 1. A quadratic equation is an equation in which the highest power of the variable is 2.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you need to use the quadratic formula, which is:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

where $a$, $b$, and $c$ are the coefficients of the quadratic equation.

Q: What is the quadratic formula?

A: The quadratic formula is a mathematical formula that is used to solve quadratic equations. It is:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

where $a$, $b$, and $c$ are the coefficients of the quadratic equation.

Q: How do I check my solution to an equation?

A: To check your solution to an equation, you need to plug it back into the original equation and see if it is true.

Q: What is the importance of checking your solution to an equation?

A: Checking your solution to an equation is important because it ensures that your solution is correct. If you don't check your solution, you may end up with an incorrect answer.

Conclusion

Solving for a variable in an equation is a fundamental concept in mathematics, and it is essential to understand how to isolate the variable to find its value. In this article, we answered some frequently asked questions about solving for a variable in an equation. We hope that this article has been helpful in clarifying any confusion you may have had about solving for a variable in an equation.

Tips and Tricks

Here are some tips and tricks to help you solve for a variable in an equation:

• Make sure to read and understand the equation before trying to solve it.
• Use inverse operations to isolate the variable on one side of the equation.
• Check your solution by plugging it back into the original equation.
• Use the quadratic formula to solve quadratic equations.

Common Mistakes

Here are some common mistakes to avoid when solving for a variable in an equation:

• Not reading and understanding the equation before trying to solve it.
• Not using inverse operations to isolate the variable on one side of the equation.
• Not checking the solution by plugging it back into the original equation.
• Not using the quadratic formula to solve quadratic equations.

Conclusion

Solving for a variable in an equation is a fundamental concept in mathematics, and it is essential to understand how to isolate the variable to find its value. In this article, we answered some frequently asked questions about solving for a variable in an equation. We hope that this article has been helpful in clarifying any confusion you may have had about solving for a variable in an equation.