Final answer:
The equivalent expression to 1/4x + 3 - 1/3x - 2 is (-1/12)x + 1 after combining like terms and finding a common denominator for the variable terms.
Step-by-step explanation:
To simplify and find an expression equivalent to 1/4x + 3 - 1/3x - 2, you would combine like terms. The terms involving x (1/4x and -1/3x) are combined by finding a common denominator, which is 12 in this case. Then, convert the constants (3 and -2) and combine them. Following these steps would lead to the equivalent expression.
Firstly, look at the variable terms:
(1/4)x = (3/12)x
- (1/3)x = -(4/12)x
Combine them:
(3/12)x - (4/12)x = (-1/12)x
Now, combine the constants:
3 - 2 = 1
The equivalent expression combines these two results:
(-1/12)x + 1