To solve the equation:

$\frac{-\frac{5}{2}}{x} - \frac{6}{5} = \frac{1}{2}$

Let's solve it step by step.

Step 1: Eliminate the fraction on the left side involving $x$.

Multiply the entire equation by $x$ to remove the denominator:

$-\frac{5}{2} - \frac{6x}{5} = \frac{x}{2}$

Step 2: Eliminate the fractions by multiplying the entire equation by the least common multiple of the denominators, which is 10.

$10 \left(-\frac{5}{2}\right) - 10\left(\frac{6x}{5}\right) = 10\left(\frac{x}{2}\right)$

Simplifying each term:

$-25 - 12x = 5x$

Step 3: Move all the terms involving $x$ to one side and constants to the other.

$-25 = 5x + 12x$

Simplify the equation:

$-25 = 17x$

Step 4: Solve for $x$.

$x = \frac{-25}{17}$

Final Answer:

$x = -\frac{25}{17}$

Would you like any more details on this solution or have any questions?

Related Questions:

1. How do you solve equations involving fractions?
2. What are the steps to clear fractions from both sides of an equation?
3. How can you verify your solution to an equation?
4. What are the key properties of equations used in this solution?
5. How do you interpret the solution to a fraction-based equation in real-world scenarios?

Tip:

When dealing with equations that have fractions, multiplying by the least common multiple of the denominators can simplify the process significantly.