Solve For R R R . 8 R + 7 = 87 R = □ \begin{array}{l} 8r + 7 = 87 \\ R = \square \end{array} 8 R + 7 = 87 R = □ ​

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a linear equation to find the value of $r$. We will break down the problem into manageable steps and provide a clear explanation of each step.

Understanding the Problem

The given problem is a linear equation in the form of $8r + 7 = 87$. Our goal is to isolate the variable $r$ and find its value. To do this, we need to follow a series of steps that will help us simplify the equation and solve for $r$.

Step 1: Subtract 7 from Both Sides

The first step in solving the equation is to subtract 7 from both sides. This will help us get rid of the constant term on the left-hand side of the equation.

8r + 7 - 7 = 87 - 7

Simplifying the equation, we get:

8r = 80

Step 2: Divide Both Sides by 8

Now that we have isolated the term with the variable $r$, we need to get rid of the coefficient 8. We can do this by dividing both sides of the equation by 8.

\frac{8r}{8} = \frac{80}{8}

Simplifying the equation, we get:

r = 10

Conclusion

In this article, we solved a linear equation to find the value of $r$. We broke down the problem into manageable steps and provided a clear explanation of each step. By following these steps, we were able to isolate the variable $r$ and find its value.

Tips and Tricks

Here are some tips and tricks to help you solve linear equations:

• Follow the order of operations: When solving an equation, make sure to follow the order of operations (PEMDAS).
• Isolate the variable: The goal of solving an equation is to isolate the variable. Make sure to get rid of any constants or coefficients that are attached to the variable.
• Check your work: Once you have solved the equation, make sure to check your work by plugging the solution back into the original equation.

Common Mistakes to Avoid

Here are some common mistakes to avoid when solving linear equations:

• Not following the order of operations: Failing to follow the order of operations can lead to incorrect solutions.
• Not isolating the variable: Failing to isolate the variable can make it difficult to solve the equation.
• Not checking your work: Failing to check your work can lead to incorrect solutions.

Real-World Applications

Linear equations have many real-world applications. Here are a few examples:

• Finance: Linear equations are used to calculate interest rates and investment returns.
• Science: Linear equations are used to model population growth and chemical reactions.
• Engineering: Linear equations are used to design and optimize systems.

Conclusion

Introduction

In our previous article, we discussed how to solve linear equations to find the value of $r$. In this article, we will provide a Q&A guide to help you better understand the concept of solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. It is a simple equation that can be solved using basic algebraic operations.

Q: What are the steps to solve a linear equation?

A: The steps to solve a linear equation are:

1. Subtract or add the same value to both sides: This helps to get rid of any constants or coefficients that are attached to the variable.
2. Multiply or divide both sides by the same value: This helps to get rid of any coefficients that are attached to the variable.
3. Isolate the variable: The goal of solving an equation is to isolate the variable. Make sure to get rid of any constants or coefficients that are attached to the variable.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when solving an equation. The order of operations is:

1. Parentheses: Evaluate any expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I check my work?

A: To check your work, plug the solution back into the original equation and make sure it is true. If the solution is not true, then you need to go back and re-solve the equation.

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

• Not following the order of operations: Failing to follow the order of operations can lead to incorrect solutions.
• Not isolating the variable: Failing to isolate the variable can make it difficult to solve the equation.
• Not checking your work: Failing to check your work can lead to incorrect solutions.

Q: How do I apply linear equations to real-world problems?

A: Linear equations have many real-world applications. Here are a few examples:

• Finance: Linear equations are used to calculate interest rates and investment returns.
• Science: Linear equations are used to model population growth and chemical reactions.
• Engineering: Linear equations are used to design and optimize systems.

Q: What are some tips and tricks for solving linear equations?

A: Here are some tips and tricks for solving linear equations:

• Use a calculator: If you are having trouble solving an equation, try using a calculator to check your work.
• Draw a diagram: Drawing a diagram can help you visualize the problem and make it easier to solve.
• Break down the problem: Breaking down the problem into smaller steps can make it easier to solve.

Conclusion

In conclusion, solving linear equations is a crucial skill for students to master. By following the steps outlined in this article and avoiding common mistakes, you can solve linear equations and apply them to real-world problems. Remember to follow the order of operations, isolate the variable, and check your work to ensure accurate solutions.