Let's solve the equation step by step:

Given equation:
\[
-6x - 3 + 8x = -7
\]

### Step 1: Combine like terms
\[
(-6x + 8x) - 3 = -7
\]
\[
2x - 3 = -7
\]

### Step 2: Add 3 to both sides to isolate the term with \(x\)
\[
2x = -7 + 3
\]
\[
2x = -4
\]

### Step 3: Divide both sides by 2 to solve for \(x\)
\[
x = \frac{-4}{2}
\]
\[
x = -2
\]

### Final solution:
\[
x = -2
\]

Would you like more details or have any questions about the solution?

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Here are 5 related questions to expand on this:
1. How do you solve equations with variables on both sides?
2. What happens when the solution to an equation is a fraction?
3. How can you check if your solution to an equation is correct?
4. What are the steps to solve an equation involving parentheses?
5. How do you solve quadratic equations?

**Tip:** Always check your solution by substituting the value back into the original equation.

This detailed step-by-step guide shows how to solve the linear equation -6x - 3 + 8x = -7. Learn how to combine like terms and use basic algebraic principles to find the value of x. Suitable for students in Grades 6-8.

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