To solve the equation \( 4x - 2 + x = 6 - 2x - 1 \), follow these steps:

### Step 1: Simplify both sides of the equation.
On the left-hand side, combine like terms:

\[
4x + x - 2 = 5x - 2
\]

On the right-hand side, simplify \( 6 - 1 \):

\[
6 - 2x - 1 = 5 - 2x
\]

Now, the equation becomes:

\[
5x - 2 = 5 - 2x
\]

### Step 2: Move all \(x\)-terms to one side.
Add \( 2x \) to both sides:

\[
5x + 2x - 2 = 5
\]

\[
7x - 2 = 5
\]

### Step 3: Isolate the \(x\)-term.
Add 2 to both sides:

\[
7x = 7
\]

### Step 4: Solve for \(x\).
Divide both sides by 7:

\[
x = 1
\]

Thus, the solution is \( x = 1 \).

Would you like further details or clarifications?

Here are some related questions:
1. How can we verify the solution of the equation?
2. How do you deal with variables on both sides of an equation?
3. What if the equation had fractions instead of integers?
4. Can you explain how to solve a system of linear equations with two variables?
5. What does it mean for an equation to have no solution?

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

Learn how to solve the linear equation 4x - 2 + x = 6 - 2x - 1 with this detailed, step-by-step guide. This solution simplifies expressions and solves for the variable x, making it a perfect problem for Grades 7-9 students practicing algebraic techniques.

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