Explanation:
To determine the number of solutions for the equation x/12 + 1 = x/3 - x/4, we can start by simplifying the equation.
First, let's find a common denominator for the fractions on the right side of the equation, which is 12:
x/12 + 1 = (4x/12) - (3x/12)
Now we can simplify the equation:
x/12 + 1 = (4x - 3x)/12
x/12 + 1 = x/12
Next, let's get rid of the denominators by multiplying both sides of the equation by 12:
12 * (x/12) + 12 * 1 = 12 * (x/12)
x + 12 = x
We can now see that the variable x cancels out on both sides of the equation:
12 = 0
Since the equation leads to a contradiction (12 = 0), there is no solution that satisfies the equation.
Therefore, the equation x/12 + 1 = x/3 - x/4 has no solution.