To determine the number of solutions for the equation 12x + 34x + 2 = 0, we first need to simplify the equation:
1. Combine like terms:
12x + 34x = 46x
So, the equation becomes:
46x + 2 = 0
2. Next, we will isolate the variable x. We do this by first moving the constant term to the other side:
46x = -2
3. Now, we solve for x by dividing both sides by 46:
x = -2/46
This simplifies to:
x = -1/23
Since this equation is linear, it only has one solution. Therefore, the number of solutions for the equation 12x + 34x + 2 = 0 is:
1 solution.