Final answer:
The correct solution to the equation 3(x - 6) = x + 14 is x = 16, not x = -1 as initially stated. After simplifying the equation, we find that the coefficient of x, denoted as a, is 2.
Step-by-step explanation:
The solution to the equation 3(x − 6) = x + 14 is given as x = -1. However, the question has been posed to determine the coefficient a in the given equation. To find a, we must first expand the equation and simplify it to its standard form ax + b = 0, by distributing the 3 into the parenthesis and moving all terms to one side to isolate x.
Expanding the equation gives us 3x - 18 = x + 14. To isolate the x terms, we subtract x from both sides resulting in 2x - 18 = 14. Adding 18 to both sides gives us 2x = 32, and by dividing both sides by 2, we find x = 16. This implies that the student's initial solution (x = -1) is incorrect. Therefore, the coefficient of x, a, in the simplified form ax = b is 2.