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The equation to solve for \( x \) is:

\[
-2 - 6y = 8x
\]

Let's solve for \( x \):

1. Start by isolating \( x \) on one side. First, divide both sides by 8:

\[
x = \frac{-2 - 6y}{8}
\]

2. Simplify the expression:

\[
x = \frac{-2}{8} - \frac{6y}{8}
\]

3. This simplifies to:

\[
x = -\frac{1}{4} - \frac{3y}{4}
\]

Thus, the solution for \( x \) is:

\[
x = -\frac{1}{4} - \frac{3y}{4}
\]

Would you like more details on any step?

Here are 5 related questions to expand on this:

1. How do we solve for \( y \) in a similar equation?
2. Can you explain how to solve linear equations with multiple variables?
3. How do we handle equations with fractions on both sides?
4. What is the geometric interpretation of this equation?
5. Can we rearrange the equation to express it in slope-intercept form?

**Tip**: When solving equations with multiple variables, try to isolate the variable of interest by using inverse operations step by step.

Learn how to solve for x in the linear equation -2 - 6y = 8x with a detailed step-by-step solution. This problem covers key algebraic concepts, including isolating variables and simplifying expressions. Suitable for students in Grades 7-9.

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