x = –12 is the solution of the linear equation 5x –3(2x + 1) = 21+x

Answer

To determine if \( x = -12 \) is the solution of the linear equation \( 5x - 3(2x + 1) = 21 + x \), we will substitute \( x \) with \(-12\) and check if both sides of the equation are equal.

### Step-by-Step Solution:

1. **Substitute \( x = -12 \) into the equation:**
\[ 5(-12) - 3(2(-12) + 1) = 21 + (-12) \]

2. **Calculate \( 5(-12) \):**
\[ 5(-12) = -60 \]

3. **Calculate \( 2(-12) + 1 \):**
\[ 2(-12) = -24 \quad \text{so} \quad -24 + 1 = -23 \]

4. **Now substitute this back into the equation:**
\[ -60 - 3(-23) = 21 - 12 \]

5. **Calculate \( -3(-23) \):**
\[ -3(-23) = 69 \]

6. **Now substitute this value back:**
\[ -60 + 69 = 21 - 12 \]

7. **Calculate both sides:**
\[ 9 = 9 \]

Since both sides of the equation are equal, we conclude that \( x = -12 \) is indeed the solution of the linear equation.

### Final Conclusion:
Thus, \( x = -12 \) is the solution of the linear equation \( 5x - 3(2x + 1) = 21 + x \).