If the linear equation (3a - 12)x + b + 7 = 0 has infinitely many solutions for x, what is the value of a + b?
(a) -3
(b) 3
(c) -11
(d) 11

Answer: A. -3

• Answer: (a) -3
• Solution:
1. A linear equation of the form Ax + B = 0 yields infinitely many solutions if and only if both the coefficient of x and the constant term are simultaneously zero (A = 0 and B = 0).
2. Set the coefficient of x to zero:
\(3a-12=0\implies 3a=12\implies a=4\)
3. Set the constant term to zero:
\(b+7=0\implies b=-7\)
4. Compute the final value:
\(a+b=4+(-7)=-3\)

Answering after opening this box earns no Practice Points.