We can use the properties of operations to rewrite the expression as follows:
-4d + 1/2 - d
First, we can apply the associative property of addition to rearrange the terms:
(-4d + 1/2) - d
Then, we can apply the distributive property to simplify the expression:
-4d + 1/2 - d
= -4d + 1/2 - 1*d
= -4d + 1/2 - d
= (-4 - 1)*d + 1/2
= -5d + 1/2
Therefore, the expression is equivalent to -5d + 1/2.
The associative property of addition states that the grouping of numbers being added does not affect the result. For example, (a + b) + c = a + (b + c).
The distributive property states that the product of a number and a group of numbers is equal to the sum of the products of the number and each individual number in the group. For example, a*(b + c) = ab + ac.