Final Answer:
The next step Carton needs to complete in order to solve the equation is option (a) Add -2 to both sides of the equation.
Step-by-step explanation:
In the provided linear equation, Carton has simplified it to 12 = -2x after combining like terms. To isolate the variable x, he needs to perform the inverse operation of the coefficient of x, which is -2. The inverse operation of subtraction is addition, so Carton should add 2 to both sides of the equation to cancel out the -2 coefficient on the right side. This results in the equation 12 + 2 = -2x + 2. By simplifying further, Carton will find the value of x. Therefore, option (a) "Add -2 to both sides of the equation" is the correct next step.
Adding -2 to both sides ensures that the equation remains balanced, and Carton is left with a simpler equation that can be easily solved. It's crucial to perform the same operation on both sides to maintain the equality of the equation. This step is a fundamental principle in solving linear equations, allowing Carton to isolate the variable and determine the solution accurately.