Solve Linear Equation: 6c+7+4c=3(c-1) Step-by-Step

To solve the equation $6c + 7 + 4c = 3(c - 1)$, follow these steps:

• Step 1: Combine like terms on the left side of the equation.
  The like terms are $6c$ and $4c$. Combining these gives $10c + 7 = 3(c - 1)$.
• Step 2: Apply the distributive property on the right side of the equation.
  The term $3(c - 1)$ expands to $3c - 3$. Therefore, the equation becomes $10c + 7 = 3c - 3$.
• Step 3: Move all terms involving $c$ to one side and constants to the other.
  Subtract $3c$ from both sides: $10c - 3c + 7 = -3$ which simplifies to $7c + 7 = -3$.
• Step 4: Isolate the term with $c$ by subtracting 7 from both sides of the equation.
  This gives $7c = -3 - 7$ or $7c = -10$.
• Step 5: Solve for $c$.
  Divide both sides by 7: $c = \frac{-10}{7} = -\frac{10}{7}$. This can be converted to a mixed number, giving $-1\frac{3}{7}$.

Therefore, the solution to the equation is $c = -1\frac{3}{7}$. This corresponds to choice 2 in the provided answer choices.