3( R -7) = 2 ( R - 5 ) What Does R Equal

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Introduction

In this article, we will be solving a linear equation involving a variable 'r'. The equation is given as 3(r - 7) = 2(r - 5). We will use algebraic techniques to isolate the variable 'r' and find its value.

Understanding the Equation

The given equation is a linear equation, which means it is an equation in which the highest power of the variable is 1. The equation is 3(r - 7) = 2(r - 5). To solve this equation, we need to isolate the variable 'r'.

Distributing the Numbers

To start solving the equation, we need to distribute the numbers outside the parentheses to the terms inside the parentheses. This means we need to multiply 3 by (r - 7) and 2 by (r - 5).

3(r - 7) = 3r - 21
2(r - 5) = 2r - 10

Setting Up the Equation

Now that we have distributed the numbers, we can set up the equation by equating the two expressions.

3r - 21 = 2r - 10

Isolating the Variable

To isolate the variable 'r', we need to get all the terms with 'r' on one side of the equation and the constant terms on the other side. We can do this by adding 21 to both sides of the equation and subtracting 2r from both sides.

3r - 2r = -10 + 21
r = 11

Conclusion

In this article, we solved the linear equation 3(r - 7) = 2(r - 5) to find the value of the variable 'r'. We used algebraic techniques to isolate the variable and found that r = 11.

Final Answer

The final answer to the equation 3(r - 7) = 2(r - 5) is r = 11.

Frequently Asked Questions

  • What is the value of r in the equation 3(r - 7) = 2(r - 5)?
  • How do we solve a linear equation involving a variable?
  • What is the first step in solving a linear equation?

Answer to Frequently Asked Questions

  • The value of r in the equation 3(r - 7) = 2(r - 5) is 11.
  • To solve a linear equation involving a variable, we need to isolate the variable by getting all the terms with the variable on one side of the equation and the constant terms on the other side.
  • The first step in solving a linear equation is to distribute the numbers outside the parentheses to the terms inside the parentheses.

Introduction

In our previous article, we solved the linear equation 3(r - 7) = 2(r - 5) to find the value of the variable 'r'. We received many questions from our readers regarding the solution and the steps involved in solving the equation. In this article, we will answer some of the frequently asked questions related to the equation.

Q&A

Q1: What is the value of r in the equation 3(r - 7) = 2(r - 5)?

A1: The value of r in the equation 3(r - 7) = 2(r - 5) is 11.

Q2: How do we solve a linear equation involving a variable?

A2: To solve a linear equation involving a variable, we need to isolate the variable by getting all the terms with the variable on one side of the equation and the constant terms on the other side. We can do this by using algebraic techniques such as adding or subtracting the same value to both sides of the equation, or multiplying or dividing both sides of the equation by the same non-zero value.

Q3: What is the first step in solving a linear equation?

A3: The first step in solving a linear equation is to distribute the numbers outside the parentheses to the terms inside the parentheses. This means we need to multiply the number outside the parentheses by each term inside the parentheses.

Q4: Can we solve the equation 3(r - 7) = 2(r - 5) using other methods?

A4: Yes, we can solve the equation 3(r - 7) = 2(r - 5) using other methods such as substitution or elimination. However, the method we used in our previous article is a simple and straightforward method that involves isolating the variable by getting all the terms with the variable on one side of the equation and the constant terms on the other side.

Q5: What is the difference between a linear equation and a quadratic equation?

A5: A linear equation is an equation in which the highest power of the variable is 1. For example, the equation 3(r - 7) = 2(r - 5) is a linear equation. A quadratic equation, on the other hand, is an equation in which the highest power of the variable is 2. For example, the equation r^2 + 4r + 4 = 0 is a quadratic equation.

Q6: Can we solve a quadratic equation using the same method we used to solve the linear equation 3(r - 7) = 2(r - 5)?

A6: No, we cannot solve a quadratic equation using the same method we used to solve the linear equation 3(r - 7) = 2(r - 5). The method we used to solve the linear equation involves isolating the variable by getting all the terms with the variable on one side of the equation and the constant terms on the other side. However, this method does not work for quadratic equations, which require more complex methods such as factoring or the quadratic formula.

Conclusion

In this article, we answered some of the frequently asked questions related to the equation 3(r - 7) = 2(r - 5). We provided step-by-step solutions to the equation and explained the concepts involved in solving linear equations. We also discussed the differences between linear and quadratic equations and how to solve them using different methods.

Final Answer

The final answer to the equation 3(r - 7) = 2(r - 5) is r = 11.

Related Articles

  • Solving Linear Equations: A Step-by-Step Guide
  • Quadratic Equations: A Comprehensive Guide
  • Algebraic Techniques for Solving Equations

Frequently Asked Questions

  • What is the value of r in the equation 3(r - 7) = 2(r - 5)?
  • How do we solve a linear equation involving a variable?
  • What is the first step in solving a linear equation?
  • Can we solve the equation 3(r - 7) = 2(r - 5) using other methods?
  • What is the difference between a linear equation and a quadratic equation?
  • Can we solve a quadratic equation using the same method we used to solve the linear equation 3(r - 7) = 2(r - 5)?