The Value Of { X $}$ Satisfies The Equation 2 X + 5 + 4 3 X = 0 \frac{2}{x+5}+\frac{4}{3x}=0 X + 5 2 ​ + 3 X 4 ​ = 0 . What Is The Value Of { -x$}$?

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Introduction

In this article, we will explore the value of {-x$}$ in a given equation. The equation provided is $\frac{2}{x+5}+\frac{4}{3x}=0$. Our goal is to find the value of {-x$}$ that satisfies this equation.

Understanding the Equation

The given equation is a rational equation, which means it contains fractions with variables in the numerator and denominator. To solve this equation, we need to find a common denominator and then combine the fractions.

Step 1: Find a Common Denominator

To find a common denominator, we need to identify the least common multiple (LCM) of the denominators. In this case, the denominators are $x+5$ and $3x$. The LCM of these two expressions is $3x(x+5)$.

Step 2: Rewrite the Equation with a Common Denominator

Now that we have a common denominator, we can rewrite the equation as follows:

$$\frac{2}{x+5}+\frac{4}{3x}=\frac{2(3x)}{3x(x+5)}+\frac{4(x+5)}{3x(x+5)}=0$$

Step 3: Combine the Fractions

We can now combine the fractions by adding the numerators:

$$\frac{6x+8(x+5)}{3x(x+5)}=0$$

Step 4: Simplify the Equation

To simplify the equation, we can expand the numerator and combine like terms:

$$\frac{6x+8x+40}{3x(x+5)}=\frac{14x+40}{3x(x+5)}=0$$

Step 5: Solve for {x$}$

Now that we have a simplified equation, we can solve for {x$}$ by setting the numerator equal to zero:

$$14x+40=0$$

Subtracting 40 from both sides gives us:

$$14x=-40$$

Dividing both sides by 14 gives us:

$$x=-\frac{40}{14}=-\frac{20}{7}$$

Finding the Value of {-x$}$

Now that we have found the value of {x$}$, we can find the value of {-x$}$ by multiplying {x$}$ by -1:

$$-x=-\left(-\frac{20}{7}\right)=\frac{20}{7}$$

Therefore, the value of {-x$}$ is $\boxed{\frac{20}{7}}$.

Conclusion

In this article, we have explored the value of {-x$}$ in a given equation. We have used algebraic techniques to simplify the equation and solve for {x$}$. Finally, we have found the value of {-x$}$ by multiplying {x$}$ by -1. The value of {-x$}$ is $\boxed{\frac{20}{7}}$.

Additional Tips and Tricks

• When solving rational equations, it is often helpful to find a common denominator and then combine the fractions.
• When simplifying equations, it is often helpful to expand the numerator and combine like terms.
• When solving for variables, it is often helpful to set the numerator equal to zero and then solve for the variable.

Real-World Applications

Rational equations have many real-world applications, including:

• Physics: Rational equations are used to describe the motion of objects and the behavior of physical systems.
• Engineering: Rational equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Rational equations are used to model economic systems and make predictions about future economic trends.

Final Thoughts

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Introduction

In our previous article, we explored the value of {-x$}$ in a given equation. We used algebraic techniques to simplify the equation and solve for {x$}$. In this article, we will answer some common questions about the value of {-x$}$ in a given equation.

Q: What is the value of {-x$}$ in the equation $\frac{2}{x+5}+\frac{4}{3x}=0$?

A: The value of {-x$}$ in the equation $\frac{2}{x+5}+\frac{4}{3x}=0$ is $\boxed{\frac{20}{7}}$.

Q: How do I find the value of {-x$}$ in a given equation?

A: To find the value of {-x$}$ in a given equation, you need to use algebraic techniques to simplify the equation and solve for {x$}$. Then, you can multiply {x$}$ by -1 to find the value of {-x$}$.

Q: What are some common mistakes to avoid when finding the value of {-x$}$ in a given equation?

A: Some common mistakes to avoid when finding the value of {-x$}$ in a given equation include:

• Not finding a common denominator when simplifying the equation
• Not combining like terms when simplifying the equation
• Not setting the numerator equal to zero when solving for {x$}$
• Not multiplying {x$}$ by -1 to find the value of {-x$}$

Q: Can you provide an example of how to find the value of {-x$}$ in a given equation?

A: Let's consider the equation $\frac{3}{x-2}+\frac{2}{x+3}=0$. To find the value of {-x$}$, we need to use algebraic techniques to simplify the equation and solve for {x$}$. Then, we can multiply {x$}$ by -1 to find the value of {-x$}$.

Step 1: Find a Common Denominator

To find a common denominator, we need to identify the least common multiple (LCM) of the denominators. In this case, the denominators are $x-2$ and $x+3$. The LCM of these two expressions is $(x-2)(x+3)$.

Step 2: Rewrite the Equation with a Common Denominator

Now that we have a common denominator, we can rewrite the equation as follows:

$$\frac{3}{x-2}+\frac{2}{x+3}=\frac{3(x+3)}{(x-2)(x+3)}+\frac{2(x-2)}{(x-2)(x+3)}=0$$

Step 3: Combine the Fractions

We can now combine the fractions by adding the numerators:

$$\frac{3(x+3)+2(x-2)}{(x-2)(x+3)}=\frac{3x+9+2x-4}{(x-2)(x+3)}=\frac{5x+5}{(x-2)(x+3)}=0$$

Step 4: Solve for {x$}$

Now that we have a simplified equation, we can solve for {x$}$ by setting the numerator equal to zero:

$$5x+5=0$$

Subtracting 5 from both sides gives us:

$$5x=-5$$

Dividing both sides by 5 gives us:

$$x=-1$$

Step 5: Find the Value of {-x$}$

Now that we have found the value of {x$}$, we can find the value of {-x$}$ by multiplying {x$}$ by -1:

$$-x=-(-1)=1$$

Therefore, the value of {-x$}$ is $\boxed{1}$.

Conclusion

In this article, we have answered some common questions about the value of {-x$}$ in a given equation. We have provided an example of how to find the value of {-x$}$ in a given equation and highlighted some common mistakes to avoid. We hope this article has been helpful in understanding the value of {-x$}$ in a given equation.

Additional Tips and Tricks

• When solving rational equations, it is often helpful to find a common denominator and then combine the fractions.
• When simplifying equations, it is often helpful to expand the numerator and combine like terms.
• When solving for variables, it is often helpful to set the numerator equal to zero and then solve for the variable.
• When finding the value of {-x$}$, it is often helpful to multiply {x$}$ by -1.

Real-World Applications

Rational equations have many real-world applications, including:

• Physics: Rational equations are used to describe the motion of objects and the behavior of physical systems.
• Engineering: Rational equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Rational equations are used to model economic systems and make predictions about future economic trends.

Final Thoughts

In conclusion, the value of {-x$}$ in a given equation can be found by using algebraic techniques to simplify the equation and solve for {x$}$. We hope this article has been helpful in understanding the value of {-x$}$ in a given equation.