- 1 over 2 ( 6 over 4 x - 2 over 3)
To simplify the expression - 1 over 2 (6 over 4 x - 2 over 3), we can begin by simplifying the expression inside the parentheses first.
6 over 4 x - 2 over 3 can be written as (6/4)x - (2/3).
To simplify further, we can find a common denominator for 4 and 3, which is 12. We then multiply the numerators by the appropriate factors to get a common denominator of 12.
This gives us (6/4)x - (2/3) = (6/4)x - (2/3)(4/4).
Simplifying the expression gives (6/4)x - (8/12).
Next, we need to find a common denominator for 4 and 12, which is 12. We then multiply the numerators by the appropriate factors to get a common denominator of 12.
This gives us (6/4)x - (8/12) = (6/4)x - (8/12)(3/3).
Simplifying the expression gives (6/4)x - (24/36).
Now, we can simplify further by canceling out any common factors in the numerators and denominators.
(6/4)x - (24/36) can be rewritten as (3/2)x - (2/3).
Finally, we can distribute the -1/2 to both terms inside the parentheses.
-1/2 (3/2)x - -1/2 (2/3) can be written as (-1/2)(3/2)x - (-1/2)(2/3).
Simplifying the expression gives us -3/4 x + 1/3.
Therefore, the simplified expression is -3/4 x + 1/3.