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The given equation to solve is:

\[
4x - 2 = 6
\]

### Step-by-step solution:

1. **Isolate the term with \(x\)**:
   Add 2 to both sides of the equation to eliminate the constant on the left side:
   \[
   4x - 2 + 2 = 6 + 2
   \]
   Simplifying:
   \[
   4x = 8
   \]

2. **Solve for \(x\)**:
   Divide both sides by 4 to isolate \(x\):
   \[
   x = \frac{8}{4}
   \]
   Simplifying:
   \[
   x = 2
   \]

### Final Answer:
\[
x = 2
\]

You can check by substituting \(x = 2\) back into the original equation:
\[
4(2) - 2 = 8 - 2 = 6
\]
Since both sides are equal, the solution is correct.

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you solve equations with variables on both sides?
2. How would you solve an equation with fractions, like \( \frac{4x}{3} - 2 = 6 \)?
3. What changes if you have an inequality instead of an equation?
4. How do you check if your solution for an equation is correct?
5. How would you solve \(4x - 2 = 6\) if you had decimals instead of integers?

**Tip:** Always perform the inverse operation to isolate the variable when solving linear equations.

Learn how to solve the linear equation 4x - 2 = 6 with a clear, step-by-step guide. This example covers essential algebraic techniques, suitable for students in grades 6-8, including isolating the variable and applying properties of equality.

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