If $$a$$ is a positive even integer and $$b$$ is a positive odd integer where $$b \gt a$$, then the number of even integers between $$a$$ and $$b$$, inclusive, must be

Correct.
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If you plug in $$a=2$$ and $$b=7$$ into this answer choice, you get
> $$\displaystyle \frac{b-a+1}{2} = \frac{7-2+1}{2} = \frac{6}{2} = 3$$
All other answer choices are eliminated for this Plug-In because they do not match your **goal value**, so this is the right answer choice.

Incorrect.
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If you plug in $$a=2$$ and $$b=7$$ into this answer choice, you get
> $$\displaystyle \frac{b-a-1}{2} = \frac{7-2-1}{2} = \frac{4}{2} = 2$$
Eliminate this answer since it doesn't match your **goal value**.

Incorrect.
[[snippet]]
If you plug in $$a=2$$ and $$b=7$$ into this answer choice, you get
> $$\displaystyle \frac{b-a}{2} = \frac{7-2}{2} = \frac{5}{2}$$
Eliminate this answer since it doesn't match your **goal value**.

Incorrect.
[[snippet]]
If you plug in $$a=2$$ and $$b=7$$ into this answer choice, you get
> $$\displaystyle {b-a} = {7-2} = 5$$
Eliminate this answer since it doesn't match your **goal value**.

Incorrect.
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If you plug in $$a=2$$ and $$b=7$$ into this answer choice, you get
> $$\displaystyle \frac{b-a+1}{2}+1 = \frac{7-2+1}{2}+1 = \frac{6}{2}+1 = 4$$
Eliminate this answer since it doesn't match your **goal value**.

$$\displaystyle \frac{b-a}{2}$$

$$\displaystyle \frac{b-a-1}{2}$$

$$\displaystyle \frac{b-a+1}{2}$$

$$\displaystyle \frac{b-a+1}{2}+1$$

$$b-a$$