Solve The Equation $r - 8.7 = 39.65$.A. $r = 30.95$ B. $r = 47.35$ C. $r = 47.72$ D. $r = 48.35$

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving a specific linear equation, $r - 8.7 = 39.65$, and explore the different methods and techniques used to find the solution.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable. Linear equations can be solved using various methods, including algebraic manipulation, graphical representation, and numerical methods.

The Equation $r - 8.7 = 39.65$

The given equation is $r - 8.7 = 39.65$. To solve for $r$, we need to isolate the variable on one side of the equation. We can do this by adding $8.7$ to both sides of the equation.

Step 1: Add 8.7 to Both Sides

r - 8.7 + 8.7 = 39.65 + 8.7

This simplifies to:

r = 48.35

Step 2: Check the Solution

To verify the solution, we can substitute $r = 48.35$ back into the original equation:

48.35 - 8.7 = 39.65

This simplifies to:

39.65 = 39.65

Since the equation holds true, we can conclude that the solution is correct.

Conclusion

Solving linear equations is an essential skill in mathematics, and it requires a clear understanding of the concepts and techniques involved. In this article, we solved the equation $r - 8.7 = 39.65$ using algebraic manipulation and verified the solution by substituting it back into the original equation. The correct solution is $r = 48.35$.

Answer

The correct answer is:

• D. $r = 48.35$

Additional Tips and Resources

• To solve linear equations, it's essential to understand the concept of inverse operations and how to apply them to isolate the variable.
• Graphical representation and numerical methods can also be used to solve linear equations, but algebraic manipulation is often the most straightforward approach.
• For more practice problems and resources, check out the following websites:
  • Khan Academy: Linear Equations
  • Mathway: Linear Equations
  • IXL: Linear Equations

Frequently Asked Questions

• Q: What is a linear equation? A: A linear equation is an equation in which the highest power of the variable(s) is 1.
• Q: How do I solve a linear equation? A: To solve a linear equation, you can use algebraic manipulation, graphical representation, or numerical methods.
• Q: What is the correct solution to the equation $r - 8.7 = 39.65$? A: The correct solution is $r = 48.35$.
  Solving Linear Equations: A Q&A Guide =====================================

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will provide a comprehensive Q&A guide to help you understand and solve linear equations.

Q: What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q: How Do I Solve a Linear Equation?

To solve a linear equation, you can use algebraic manipulation, graphical representation, or numerical methods. Here are the steps to solve a linear equation:

1. Isolate the variable: Move all the terms with the variable to one side of the equation.
2. Apply inverse operations: Use inverse operations to isolate the variable.
3. Simplify the equation: Simplify the equation to find the value of the variable.

Q: What is the Difference Between a Linear Equation and a Non-Linear Equation?

A linear equation is an equation in which the highest power of the variable(s) is 1. A non-linear equation, on the other hand, is an equation in which the highest power of the variable(s) is greater than 1.

Q: How Do I Graph a Linear Equation?

To graph a linear equation, you can use the following steps:

1. Find the x-intercept: Find the value of x when y is equal to 0.
2. Find the y-intercept: Find the value of y when x is equal to 0.
3. Plot the points: Plot the points on a coordinate plane.
4. Draw the line: Draw a line through the points to represent the linear equation.

Q: What is the Slope-Intercept Form of a Linear Equation?

The slope-intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Q: How Do I Find the Slope of a Linear Equation?

To find the slope of a linear equation, you can use the following formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.

Q: What is the Point-Slope Form of a Linear Equation?

The point-slope form of a linear equation is $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope.

Q: How Do I Solve a System of Linear Equations?

To solve a system of linear equations, you can use the following methods:

1. Substitution method: Substitute one equation into the other equation to solve for the variable.
2. Elimination method: Add or subtract the equations to eliminate one variable.
3. Graphical method: Graph the equations on a coordinate plane and find the point of intersection.

Conclusion

Solving linear equations is an essential skill in mathematics, and it requires a clear understanding of the concepts and techniques involved. In this article, we provided a comprehensive Q&A guide to help you understand and solve linear equations. Whether you're a student or a professional, this guide will help you master the art of solving linear equations.

Additional Tips and Resources

• To solve linear equations, it's essential to understand the concept of inverse operations and how to apply them to isolate the variable.
• Graphical representation and numerical methods can also be used to solve linear equations, but algebraic manipulation is often the most straightforward approach.
• For more practice problems and resources, check out the following websites:
  • Khan Academy: Linear Equations
  • Mathway: Linear Equations
  • IXL: Linear Equations

Frequently Asked Questions

• Q: What is a linear equation? A: A linear equation is an equation in which the highest power of the variable(s) is 1.
• Q: How do I solve a linear equation? A: To solve a linear equation, you can use algebraic manipulation, graphical representation, or numerical methods.
• Q: What is the difference between a linear equation and a non-linear equation? A: A linear equation is an equation in which the highest power of the variable(s) is 1, while a non-linear equation is an equation in which the highest power of the variable(s) is greater than 1.