What is the solution set of the equation
`x + 6 = 2(x + 3) -x`?

Options

A. The empty set (no solution)
B. {0}
C. {2}
D. The set of all real numbers

Answer

To solve the equation \( x + 6 = 2(x + 3) - x \), we will simplify and analyze the equation step by step.

### Step 1: Expand the right-hand side
Start with the equation:
\[ x + 6 = 2(x + 3) - x \]
Now, expand the term \( 2(x + 3) \):
\[ 2(x + 3) = 2x + 6 \]
So, the equation becomes:
\[ x + 6 = 2x + 6 - x \]

### Step 2: Simplify the right-hand side
Now simplify the right-hand side:
\[ 2x + 6 - x = x + 6 \]
Thus, the equation now looks like:
\[ x + 6 = x + 6 \]

### Step 3: Analyze the equation
Notice that both sides of the equation are identical:
\[ x + 6 = x + 6 \]
This means that the equation holds true for any value of \( x \).

### Conclusion
Since the equation is true for all real numbers, the solution set is the set of all real numbers.

Thus, the solution set is:
\[ \text{Solution set} = \mathbb{R} \quad (\text{the set of all real numbers}) \]