To determine how many solutions exist for the equation, we need to simplify it first. The equation is:
12x + 34x + 2 = 0
Combine the like terms (the terms with ‘x’):
(12 + 34)x + 2 = 0
This simplifies to:
46x + 2 = 0
Next, we isolate ‘x’. Start by subtracting 2 from both sides:
46x = -2
Now, divide by 46:
x = -2/46
Reducing this fraction gives:
x = -1/23
This shows that there is exactly one solution to the equation, which is x = -1/23. Therefore, the answer to the question is that there exists only one solution for the given equation.