Solve The Equation:$ \frac{2x}{2x-15} = \frac{3}{5} }$Choose The Correct Value Of { X $}$ A. { X = -11.25 $ $B. { X = -9 $}$C. { X = -3.75 $}$D. { X = -0.9375 $}$

Introduction

In this article, we will be solving a complex equation involving fractions and variables. The equation is given as $\frac{2x}{2x-15} = \frac{3}{5}$, and we need to find the correct value of $x$ from the given options. We will break down the solution into manageable steps, making it easy to understand and follow.

Step 1: Cross-Multiplication

The first step in solving this equation is to cross-multiply the fractions. This means multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa. The equation becomes:

$$5(2x) = 3(2x-15)$$

Step 2: Distributing the Numbers

Next, we need to distribute the numbers inside the parentheses. This means multiplying each term inside the parentheses by the number outside. The equation becomes:

$$10x = 6x - 45$$

Step 3: Subtracting 6x from Both Sides

To isolate the variable $x$, we need to get all the terms with $x$ on one side of the equation. We can do this by subtracting $6x$ from both sides of the equation. The equation becomes:

$$4x = -45$$

Step 4: Dividing Both Sides by 4

Finally, we need to solve for $x$ by dividing both sides of the equation by 4. The equation becomes:

$$x = -\frac{45}{4}$$

Simplifying the Fraction

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 5. The equation becomes:

$$x = -\frac{9}{4}$$

Converting the Fraction to a Decimal

To convert the fraction to a decimal, we can divide the numerator by the denominator. The equation becomes:

$$x = -2.25$$

Comparing the Solutions

Now that we have solved the equation, we can compare our solution to the given options. The correct value of $x$ is:

$$x = -2.25$$

However, this value is not among the given options. Let's re-examine the steps we took to solve the equation.

Re-examining the Steps

Upon re-examining the steps, we realize that we made an error in our calculations. The correct solution is:

$$x = -\frac{45}{4}$$

Simplifying the Fraction

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 5. The equation becomes:

$$x = -\frac{9}{4}$$

Converting the Fraction to a Decimal

To convert the fraction to a decimal, we can divide the numerator by the denominator. The equation becomes:

$$x = -2.25$$

However, we can also express this value as a decimal with more precision. The equation becomes:

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Q: What is the correct value of x in the equation $\frac{2x}{2x-15} = \frac{3}{5}$?

A: The correct value of x is $x = -\frac{45}{4}$.

Q: How do I simplify the fraction $-\frac{45}{4}$?

A: To simplify the fraction, you can divide both the numerator and the denominator by their greatest common divisor, which is 5. The simplified fraction is $-\frac{9}{4}$.

Q: How do I convert the fraction $-\frac{9}{4}$ to a decimal?

A: To convert the fraction to a decimal, you can divide the numerator by the denominator. The decimal equivalent of $-\frac{9}{4}$ is $-2.25$.

Q: Why is the decimal equivalent of $-\frac{9}{4}$ not among the given options?

A: The decimal equivalent of $-\frac{9}{4}$ is $-2.25$, which is not among the given options. However, we can express this value as a decimal with more precision.

Q: How do I express the decimal $-2.25$ with more precision?

A: You can express the decimal $-2.25$ with more precision by using a repeating decimal or a fraction. For example, you can express $-2.25$ as $-\frac{9}{4}$ or $-2.25 = -\frac{9}{4}$.

Q: What are the given options for the value of x?

A: The given options for the value of x are:

A. $x = -11.25$ B. $x = -9$ C. $x = -3.75$ D. $x = -0.9375$

Q: Which of the given options is the correct value of x?

A: The correct value of x is not among the given options. However, we can see that the value $x = -2.25$ is close to the value $x = -2.25 = -\frac{9}{4}$.

Q: Why is the value $x = -2.25$ not among the given options?

A: The value $x = -2.25$ is not among the given options because it is not a precise match for the value $x = -\frac{9}{4}$. However, we can see that the value $x = -2.25$ is a close approximation of the value $x = -\frac{9}{4}$.

Q: What is the best way to solve the equation $\frac{2x}{2x-15} = \frac{3}{5}$?

A: The best way to solve the equation is to follow the steps outlined in the previous section. This includes cross-multiplying, distributing the numbers, subtracting 6x from both sides, and dividing both sides by 4.

Q: What are some common mistakes to avoid when solving the equation $\frac{2x}{2x-15} = \frac{3}{5}$?

A: Some common mistakes to avoid when solving the equation include:

• Not cross-multiplying the fractions
• Not distributing the numbers correctly
• Not subtracting 6x from both sides
• Not dividing both sides by 4
• Not simplifying the fraction correctly

Q: How can I practice solving equations like $\frac{2x}{2x-15} = \frac{3}{5}$?

A: You can practice solving equations like $\frac{2x}{2x-15} = \frac{3}{5}$ by working through multiple examples and exercises. You can also try solving equations with different variables and coefficients.