Let's solve the equation step by step:

Given equation: $9(x - 2) + x = 2x + 6$

Step 1: Distribute the $9$ on the left-hand side.

$9(x - 2) = 9x - 18$ So, the equation becomes: $9x - 18 + x = 2x + 6$

Step 2: Combine like terms on both sides.

On the left-hand side: $9x + x = 10x$ Thus, the equation simplifies to: $10x - 18 = 2x + 6$

Step 3: Move all terms involving $x$ to one side.

Subtract $2x$ from both sides: $10x - 2x - 18 = 6$ This simplifies to: $8x - 18 = 6$

Step 4: Move the constant terms to the other side.

Add $18$ to both sides: $8x = 6 + 18$ This simplifies to: $8x = 24$

Step 5: Solve for $x$.

Divide both sides by $8$: $x = \frac{24}{8} = 3$

Final Answer:

The solution is $x = 3$.

Would you like more details, or do you have any further questions?

Here are 5 related questions for practice:

1. Solve: $5(x + 4) + 3x = 6x + 20$
2. Solve: $2(x - 5) - 4x = 3 - x$
3. What is the value of $x$ in the equation $7x - 3 = 2x + 12$?
4. Simplify and solve: $12(x + 2) = 3(4x + 8)$
5. Find $x$: $8x + 6 = 2x - 12$

Tip: Always start by simplifying each side of the equation before moving terms across the equals sign.