Kiemanh Is Solving The Equation 15 R − 6 R = 36 15r - 6r = 36 15 R − 6 R = 36 . What Is The Value Of R R R ?A. 2 B. 4 C. 15 D. 27

Introduction

In mathematics, equations are a fundamental concept that helps us understand and solve problems. One of the most common types of equations is a linear equation, which is an equation in which the highest power of the variable is 1. In this article, we will solve the equation $15r - 6r = 36$ step by step, and find the value of $r$.

Understanding the Equation

The given equation is $15r - 6r = 36$. To solve this equation, we need to isolate the variable $r$. The first step is to combine like terms on the left-hand side of the equation.

Combining Like Terms

When we combine like terms, we add or subtract the coefficients of the same variables. In this case, we have two terms with the variable $r$: $15r$ and $-6r$. To combine these terms, we add their coefficients:

$$15r - 6r = (15 - 6)r = 9r$$

So, the equation becomes:

$$9r = 36$$

Isolating the Variable

Now that we have combined like terms, we need to isolate the variable $r$. To do this, we divide both sides of the equation by the coefficient of $r$, which is 9.

$$\frac{9r}{9} = \frac{36}{9}$$

This simplifies to:

$$r = 4$$

Conclusion

Therefore, the value of $r$ is 4.

Why is this Important?

Solving equations is an essential skill in mathematics, and it has many real-world applications. In science, technology, engineering, and mathematics (STEM) fields, equations are used to model and solve problems. For example, in physics, equations are used to describe the motion of objects, while in economics, equations are used to model the behavior of markets.

Tips and Tricks

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

• Combine like terms: When you have multiple terms with the same variable, combine them by adding or subtracting their coefficients.
• Isolate the variable: To isolate the variable, divide both sides of the equation by the coefficient of the variable.
• Check your work: Always check your work by plugging the solution back into the original equation.

Conclusion

In conclusion, solving the equation $15r - 6r = 36$ is a simple process that involves combining like terms and isolating the variable. By following these steps, we can find the value of $r$, which is 4. This equation is a great example of how mathematics can be used to solve real-world problems.

Frequently Asked Questions

Q: What is the value of $r$ in the equation $15r - 6r = 36$?

A: The value of $r$ is 4.

Q: How do I combine like terms in an equation?

A: To combine like terms, add or subtract the coefficients of the same variables.

Q: How do I isolate the variable in an equation?

A: To isolate the variable, divide both sides of the equation by the coefficient of the variable.

Q: Why is solving equations important?

A: Solving equations is an essential skill in mathematics, and it has many real-world applications in science, technology, engineering, and mathematics (STEM) fields.

References

• Mathematics
• Equations
• Linear Equations

Related Articles

• Solving Quadratic Equations
• Solving Systems of Equations
• Graphing Equations
  Frequently Asked Questions: Solving Equations =====================================================

Introduction

Solving equations is a fundamental concept in mathematics that helps us understand and solve problems. In this article, we will answer some frequently asked questions about solving equations, including how to combine like terms, how to isolate the variable, and why solving equations is important.

Q&A

Q: What is the value of $r$ in the equation $15r - 6r = 36$?

A: The value of $r$ is 4.

Q: How do I combine like terms in an equation?

A: To combine like terms, add or subtract the coefficients of the same variables. For example, in the equation $15r - 6r = 36$, we can combine the like terms by adding the coefficients:

$$15r - 6r = (15 - 6)r = 9r$$

Q: How do I isolate the variable in an equation?

A: To isolate the variable, divide both sides of the equation by the coefficient of the variable. For example, in the equation $9r = 36$, we can isolate the variable by dividing both sides by 9:

$$\frac{9r}{9} = \frac{36}{9}$$

This simplifies to:

$$r = 4$$

Q: Why is solving equations important?

A: Solving equations is an essential skill in mathematics, and it has many real-world applications in science, technology, engineering, and mathematics (STEM) fields. Equations are used to model and solve problems in fields such as physics, economics, and computer science.

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. For example, the equation $2x + 3 = 5$ 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 $x^2 + 4x + 4 = 0$ is a quadratic equation.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you can use the quadratic formula:

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

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

Q: What is the difference between a system of equations and a single equation?

A: A system of equations is a set of two or more equations that are solved simultaneously. For example, the system of equations:

$$x + y = 2$$

$$x - y = 1$$

can be solved simultaneously to find the values of $x$ and $y$.

A single equation, on the other hand, is a single equation that is solved independently. For example, the equation $x + 2 = 4$ is a single equation that can be solved independently to find the value of $x$.

Q: How do I graph an equation?

A: To graph an equation, you can use a graphing calculator or a computer program. You can also graph an equation by plotting points on a coordinate plane and drawing a line through the points.

Conclusion

In conclusion, solving equations is a fundamental concept in mathematics that helps us understand and solve problems. By following the steps outlined in this article, you can solve equations and answer frequently asked questions about solving equations.

Frequently Asked Questions: Solving Equations (continued)

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

A: A linear equation is an equation in which the highest power of the variable is 1. A nonlinear equation, on the other hand, is an equation in which the highest power of the variable is greater than 1.

Q: How do I solve a nonlinear equation?

A: To solve a nonlinear equation, you can use numerical methods such as the Newton-Raphson method or the bisection method.

Q: What is the difference between a system of linear equations and a system of nonlinear equations?

A: A system of linear equations is a set of two or more linear equations that are solved simultaneously. A system of nonlinear equations, on the other hand, is a set of two or more nonlinear equations that are solved simultaneously.

Q: How do I solve a system of nonlinear equations?

A: To solve a system of nonlinear equations, you can use numerical methods such as the Newton-Raphson method or the bisection method.

References

• Mathematics
• Equations
• Linear Equations
• Quadratic Equations
• Systems of Equations

Related Articles

• Solving Quadratic Equations
• Solving Systems of Equations
• Graphing Equations
• Numerical Methods for Solving Equations