Completely <math xmlns="http://www.w3.org/1998/Math/MathML">
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        <mi>x</mi>
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</math>simplify your answer

To solve the equation \(-\frac{5}{2x} - 1 = \frac{1}{6x}\), we need to isolate the variable \(x\). Here are the steps:

1. Start with the given equation:
\[
-\frac{5}{2x} - 1 = \frac{1}{6x}
\]

2. Combine the fractions by finding a common denominator. The common denominator of \(2x\) and \(6x\) is \(6x\). Rewrite each term with the common denominator:
\[
-\frac{5 \cdot 3}{6x} - 1 = \frac{1}{6x}
\]
\[
-\frac{15}{6x} - 1 = \frac{1}{6x}
\]

3. Combine the fractions on the left side:
\[
-\frac{15}{6x} - 1 = \frac{1}{6x}
\]

4. Move all terms to one side of the equation to combine like terms:
\[
-\frac{15}{6x} - 1 - \frac{1}{6x} = 0
\]
\[
-\frac{15}{6x} - \frac{1}{6x} - 1 = 0
\]

5. Combine the fractions on the left side:
\[
-\frac{15 + 1}{6x} - 1 = 0
\]
\[
-\frac{16}{6x} - 1 = 0
\]

6. Simplify the fraction:
\[
-\frac{8}{3x} - 1 = 0
\]

7. Move \(-1\) to the other side of the equation:
\[
-\frac{8}{3x} = 1
\]

8. Multiply both sides by \(-1\):
\[
\frac{8}{3x} = -1
\]

9. Cross-multiply to solve for \(x\):
\[
8 = -3x
\]

10. Divide both sides by \(-3\):
\[
x = -\frac{8}{3}
\]

So, the solution to the equation is:
\[
x = -\frac{8}{3}
\]

Would you like any further details or have any questions about this solution? 

Here are 5 questions you might consider asking next:
1. How do you solve quadratic equations?
2. What are the steps for solving a system of linear equations?
3. Can you explain the process of factoring polynomials?
4. How do you find the derivative of a function?
5. What are the methods for solving inequalities?

**Tip:** When solving equations involving fractions, finding a common denominator can simplify the process of combining terms and isolating variables.

Learn how to solve the equation -5/(2x) - 1 = 1/(6x) with a detailed step-by-step solution. This problem covers equations involving fractions and variables. Suitable for high school students.

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