Simplify The Equation:\[$\frac{10}{9} = 5x\$\]Find \[$x\$\]: $\[x = \\]

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Introduction

Simplifying equations is a fundamental concept in mathematics, and it is essential to understand how to manipulate algebraic expressions to solve for unknown variables. In this article, we will focus on simplifying the equation $\frac{10}{9} = 5x$ and finding the value of $x$. We will break down the steps involved in simplifying the equation and provide a clear explanation of each step.

Understanding the Equation

The given equation is $\frac{10}{9} = 5x$. This equation states that the fraction $\frac{10}{9}$ is equal to $5$ times the variable $x$. To simplify the equation, we need to isolate the variable $x$ and find its value.

Step 1: Multiply Both Sides by 5

To isolate the variable $x$, we need to get rid of the coefficient $5$ that is multiplied by $x$. We can do this by multiplying both sides of the equation by $5$. This will cancel out the $5$ on the right-hand side of the equation.

$\frac{10}{9} = 5x$

$\frac{10}{9} \times 5 = 5x \times 5$

$\frac{50}{9} = 25x$

Step 2: Multiply Both Sides by $\frac{9}{50}$

To isolate the variable $x$, we need to get rid of the fraction $\frac{50}{9}$ that is multiplied by $x$. We can do this by multiplying both sides of the equation by the reciprocal of $\frac{50}{9}$, which is $\frac{9}{50}$.

$\frac{50}{9} = 25x$

$\frac{50}{9} \times \frac{9}{50} = 25x \times \frac{9}{50}$

$1 = \frac{225}{50}x$

Step 3: Simplify the Right-Hand Side

To simplify the right-hand side of the equation, we can divide the numerator and denominator by their greatest common divisor, which is $25$.

$1 = \frac{225}{50}x$

$1 = \frac{9}{2}x$

Step 4: Multiply Both Sides by $\frac{2}{9}$

To isolate the variable $x$, we need to get rid of the fraction $\frac{9}{2}$ that is multiplied by $x$. We can do this by multiplying both sides of the equation by the reciprocal of $\frac{9}{2}$, which is $\frac{2}{9}$.

$1 = \frac{9}{2}x$

$1 \times \frac{2}{9} = \frac{9}{2}x \times \frac{2}{9}$

$\frac{2}{9} = x$

Conclusion

In this article, we simplified the equation $\frac{10}{9} = 5x$ and found the value of $x$. We broke down the steps involved in simplifying the equation and provided a clear explanation of each step. By following these steps, we were able to isolate the variable $x$ and find its value.

Final Answer

The final answer is $\boxed{\frac{2}{9}}$.

Related Topics

• Simplifying algebraic expressions
• Solving linear equations
• Isolating variables

Further Reading

• Simplifying Algebraic Expressions
• Solving Linear Equations
• Isolating Variables
  

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Introduction

In our previous article, we simplified the equation $\frac{10}{9} = 5x$ and found the value of $x$. However, we understand that some readers may still have questions about the steps involved in simplifying the equation. In this article, we will address some of the most frequently asked questions about simplifying the equation $\frac{10}{9} = 5x$.

Q&A

Q: What is the first step in simplifying the equation $\frac{10}{9} = 5x$?

A: The first step in simplifying the equation $\frac{10}{9} = 5x$ is to multiply both sides of the equation by $5$. This will cancel out the $5$ on the right-hand side of the equation.

Q: Why do we multiply both sides of the equation by $5$?

A: We multiply both sides of the equation by $5$ to get rid of the coefficient $5$ that is multiplied by $x$. This will allow us to isolate the variable $x$.

Q: What is the next step in simplifying the equation $\frac{10}{9} = 5x$?

A: The next step in simplifying the equation $\frac{10}{9} = 5x$ is to multiply both sides of the equation by the reciprocal of $\frac{50}{9}$, which is $\frac{9}{50}$. This will cancel out the fraction $\frac{50}{9}$ that is multiplied by $x$.

Q: Why do we multiply both sides of the equation by the reciprocal of $\frac{50}{9}$?

A: We multiply both sides of the equation by the reciprocal of $\frac{50}{9}$ to get rid of the fraction $\frac{50}{9}$ that is multiplied by $x$. This will allow us to isolate the variable $x$.

Q: What is the final step in simplifying the equation $\frac{10}{9} = 5x$?

A: The final step in simplifying the equation $\frac{10}{9} = 5x$ is to multiply both sides of the equation by the reciprocal of $\frac{9}{2}$, which is $\frac{2}{9}$. This will cancel out the fraction $\frac{9}{2}$ that is multiplied by $x$ and give us the value of $x$.

Q: Why do we multiply both sides of the equation by the reciprocal of $\frac{9}{2}$?

A: We multiply both sides of the equation by the reciprocal of $\frac{9}{2}$ to get rid of the fraction $\frac{9}{2}$ that is multiplied by $x$. This will give us the value of $x$.

Q: What is the value of $x$?

A: The value of $x$ is $\frac{2}{9}$.

Conclusion

In this article, we addressed some of the most frequently asked questions about simplifying the equation $\frac{10}{9} = 5x$. We provided clear explanations of each step involved in simplifying the equation and answered questions about the process.

Final Answer

The final answer is $\boxed{\frac{2}{9}}$.

Related Topics

• Simplifying algebraic expressions
• Solving linear equations
• Isolating variables

Further Reading

• Simplifying Algebraic Expressions
• Solving Linear Equations
• Isolating Variables