To solve the equation \(2x + 1 - 3c = 2c + 3x - 7\) given that \(x = -2\) is a solution, we will substitute \(-2\) for \(x\) and then solve for \(c\). ### Step-by-Step Solution: 1. **Substituting the value of \(x\)**: We start by substituting \(-2\) into the equation: \[ 2(-2) + 1 - 3c = 2c + 3(-2) - 7 \] 2. **Calculating the left side**: \[ 2(-2) + 1 = -4 + 1 = -3 \] So, the left side becomes: \[ -3 - 3c \] 3. **Calculating the right side**: \[ 3(-2) = -6 \] Therefore, the right side becomes: \[ 2c - 6 - 7 = 2c - 13 \] 4. **Setting the left side equal to the right side**: Now we have: \[ -3 - 3c = 2c - 13 \] 5. **Rearranging the equation**: To isolate \(c\), we can first add \(3c\) to both sides: \[ -3 = 2c + 3c - 13 \] This simplifies to: \[ -3 = 5c - 13 \] 6. **Adding 13 to both sides**: \[ -3 + 13 = 5c \] This simplifies to: \[ 10 = 5c \] 7. **Dividing by 5**: \[ c = \frac{10}{5} = 2 \] ### Conclusion: The value of \(c\) is \(2\). Therefore, the correct option is **C. 2**. ### Explanation of Other Options: - **Option A (4)**: If \(c = 4\), substituting back into the equation would not satisfy the equality, as shown in the calculations. - **Option B (3)**: Similarly, if \(c = 3\), the left and right sides of the equation would not balance. - **Option D (1)**: If \(c = 1\), the equation would also not hold true upon substitution. ### Common Pitfalls: - **Miscalculating the substitution**: Always double-check arithmetic when substituting values. - **Forgetting to combine like terms**: Ensure that all terms involving \(c\) are correctly combined. - **Sign errors**: Be careful with negative signs, especially when moving terms from one side of the equation to the other. ### Revision Summary: - Substitute the given solution into the equation. - Rearrange the equation to isolate the variable \(c\). - Solve for \(c\) and verify by substituting back into the original equation. - Check all options to confirm which one satisfies the equation.