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To solve the equation:

\[
6 - 7x = 6x - 8x - 14
\]

let's go through the steps:

### Step 1: Simplify each side
Combine like terms on the right side:
\[
6 - 7x = -2x - 14
\]

### Step 2: Move terms involving \( x \) to one side
Add \( 7x \) to both sides to isolate terms with \( x \) on the right side:
\[
6 = 5x - 14
\]

### Step 3: Move constant terms to the other side
Add \( 14 \) to both sides to isolate the term with \( x \) on the right:
\[
20 = 5x
\]

### Step 4: Solve for \( x \)
Divide both sides by \( 5 \) to find \( x \):
\[
x = 4
\]

### Final Answer
The value of \( x \) is \( 4 \).

Would you like further details or have any questions?

### Further Related Questions
1. How do you combine like terms in an equation?
2. What steps can help isolate the variable in linear equations?
3. Why do we add or subtract terms from both sides of the equation?
4. How can we verify our solution for \( x \)?
5. What if the equation involved fractions instead of whole numbers?

### Tip
Always check your solution by plugging it back into the original equation to ensure both sides are equal.

Solve 6 - 7x = 6x - 8x - 14. The value of x is __.

Learn how to solve the linear equation 6 - 7x = 6x - 8x - 14 with step-by-step instructions. This problem involves combining like terms and isolating the variable, ideal for students in Grades 7-9.

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