Final answer:
To rewrite the expression 3 - 4 using the additive inverse, one would look for an expression that adds -4 to 3, giving 3 + (-4). The options provided in the question do not include the correct representation; therefore, none of the available choices correctly rewrite the expression using the additive inverse.
Step-by-step explanation:
The question is asking for the correct representation of the expression 3 - 4 using the additive inverse and how to display it on a number line. To find the additive inverse, we would look for an expression that effectively gives us the same result as subtracting 4 from 3, but by adding its inverse counterpart.
To do this, we need to recognize that the additive inverse of a number is what we add to the original number to get zero. The additive inverse of 4 is -4, and thus, to rewrite 3 - 4, we would be looking for an expression that adds -4 to 3. Therefore, the correct expression would be 3 + (-4), which is mathematically equivalent to 3 - 4.
However, the options given in the question do not include 3 + (-4) directly. We must look for an equivalent expression. The closest equivalent option provided is a) -3 + 4, which is not correct because
Option b) 4 - 3 does not involve the additive inverse of 4, it simply subtracts 3 from 4.
Option c) -3 - 4 would mean we're subtracting 4 from -3, which is not the same as 3 - 4.
Option d) 3 + 4 would add 4 to 3, which again, is not the same as subtracting 4 from 3.
Therefore, none of the options provided correctly rewrite the expression 3 - 4 using the additive inverse and represent it on a number line. The correct answer might be a rewriting of 3 - 4 as 3 + (-4), but this is not available in the options given.