Solve For $r$.$0 = \frac{r-10}{-2}$$r = $[/tex]

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Introduction

In mathematics, solving for a variable is a fundamental concept that involves isolating the variable on one side of the equation. In this article, we will focus on solving for the variable r in the equation 0 = (r-10)/(-2). This equation is a simple linear equation that can be solved using basic algebraic techniques.

Understanding the Equation

The given equation is 0 = (r-10)/(-2). To solve for r, we need to isolate r on one side of the equation. The equation can be rewritten as 0 = r - 10/-2. This can be further simplified to 0 = r + 5.

Solving for r

To solve for r, we need to isolate r on one side of the equation. We can do this by subtracting 5 from both sides of the equation. This gives us -5 = r.

Conclusion

In conclusion, solving for r in the equation 0 = (r-10)/(-2) involves isolating r on one side of the equation. By subtracting 5 from both sides of the equation, we can solve for r and find that r = -5.

Step-by-Step Solution

Step 1: Rewrite the Equation

The given equation is 0 = (r-10)/(-2). We can rewrite this equation as 0 = r - 10/-2.

Step 2: Simplify the Equation

We can simplify the equation by combining the constants on the right-hand side. This gives us 0 = r + 5.

Step 3: Isolate r

To isolate r, we need to get rid of the constant term on the right-hand side. We can do this by subtracting 5 from both sides of the equation. This gives us -5 = r.

Example Problems

Problem 1

Solve for x in the equation 0 = (x-3)/(-4).

Solution

We can rewrite the equation as 0 = x - 3/-4. This can be further simplified to 0 = x + 3/4. To solve for x, we need to isolate x on one side of the equation. We can do this by subtracting 3/4 from both sides of the equation. This gives us -3/4 = x.

Problem 2

Solve for y in the equation 0 = (y-2)/(-3).

Solution

We can rewrite the equation as 0 = y - 2/-3. This can be further simplified to 0 = y + 2/3. To solve for y, we need to isolate y on one side of the equation. We can do this by subtracting 2/3 from both sides of the equation. This gives us -2/3 = y.

Tips and Tricks

Tip 1: Simplify the Equation

When solving for a variable, it's essential to simplify the equation as much as possible. This can make it easier to isolate the variable and solve for it.

Tip 2: Isolate the Variable

To solve for a variable, you need to isolate it on one side of the equation. This can be done by adding or subtracting the same value from both sides of the equation.

Tip 3: Check Your Work

Once you've solved for a variable, it's essential to check your work to ensure that the solution is correct. This can be done by plugging the solution back into the original equation and verifying that it's true.

Real-World Applications

Solving for a variable is a fundamental concept in mathematics that has numerous real-world applications. Here are a few examples:

  • Physics: In physics, solving for a variable is essential in calculating distances, velocities, and accelerations.
  • Engineering: In engineering, solving for a variable is crucial in designing and building structures, such as bridges and buildings.
  • Economics: In economics, solving for a variable is essential in understanding and analyzing economic data.

Conclusion

In conclusion, solving for a variable is a fundamental concept in mathematics that involves isolating the variable on one side of the equation. By following the steps outlined in this article, you can solve for a variable and apply the concept to real-world problems. Whether you're a student or a professional, understanding how to solve for a variable is essential in mathematics and has numerous real-world applications.

Introduction

In our previous article, we discussed how to solve for the variable r in the equation 0 = (r-10)/(-2). In this article, we will provide a Q&A section to help clarify any doubts or questions that readers may have.

Q&A

Q: What is the first step in solving for r in the equation 0 = (r-10)/(-2)?

A: The first step in solving for r is to rewrite the equation as 0 = r - 10/-2.

Q: How do I simplify the equation 0 = r - 10/-2?

A: To simplify the equation, we can combine the constants on the right-hand side. This gives us 0 = r + 5.

Q: How do I isolate r in the equation 0 = r + 5?

A: To isolate r, we need to get rid of the constant term on the right-hand side. We can do this by subtracting 5 from both sides of the equation. This gives us -5 = r.

Q: What if the equation is 0 = (x-3)/(-4)? How do I solve for x?

A: To solve for x, we can rewrite the equation as 0 = x - 3/-4. This can be further simplified to 0 = x + 3/4. To solve for x, we need to isolate x on one side of the equation. We can do this by subtracting 3/4 from both sides of the equation. This gives us -3/4 = x.

Q: What if the equation is 0 = (y-2)/(-3)? How do I solve for y?

A: To solve for y, we can rewrite the equation as 0 = y - 2/-3. This can be further simplified to 0 = y + 2/3. To solve for y, we need to isolate y on one side of the equation. We can do this by subtracting 2/3 from both sides of the equation. This gives us -2/3 = y.

Q: What are some real-world applications of solving for a variable?

A: Solving for a variable has numerous real-world applications, including physics, engineering, and economics. In physics, solving for a variable is essential in calculating distances, velocities, and accelerations. In engineering, solving for a variable is crucial in designing and building structures, such as bridges and buildings. In economics, solving for a variable is essential in understanding and analyzing economic data.

Q: How do I check my work when solving for a variable?

A: To check your work, you can plug the solution back into the original equation and verify that it's true. This ensures that the solution is correct and helps to build confidence in your problem-solving skills.

Tips and Tricks

Tip 1: Simplify the Equation

When solving for a variable, it's essential to simplify the equation as much as possible. This can make it easier to isolate the variable and solve for it.

Tip 2: Isolate the Variable

To solve for a variable, you need to isolate it on one side of the equation. This can be done by adding or subtracting the same value from both sides of the equation.

Tip 3: Check Your Work

Once you've solved for a variable, it's essential to check your work to ensure that the solution is correct. This can be done by plugging the solution back into the original equation and verifying that it's true.

Conclusion

In conclusion, solving for a variable is a fundamental concept in mathematics that involves isolating the variable on one side of the equation. By following the steps outlined in this article and using the Q&A section to clarify any doubts or questions, you can solve for a variable and apply the concept to real-world problems. Whether you're a student or a professional, understanding how to solve for a variable is essential in mathematics and has numerous real-world applications.