Let's solve the expression step-by-step for [tex]\( g = -3.5 \)[/tex].
1. First, substitute [tex]\( g = -3.5 \)[/tex] into the expression [tex]\( 2g - 5 \)[/tex]:
[tex]\[
2(-3.5) - 5
\][/tex]
2. Multiply [tex]\( 2 \)[/tex] by [tex]\( -3.5 \)[/tex]:
[tex]\[
2 \times -3.5 = -7
\][/tex]
3. Then, subtract [tex]\( 5 \)[/tex] from [tex]\( -7 \)[/tex]:
[tex]\[
-7 - 5 = -12
\][/tex]
So, the value of the inner expression [tex]\( 2g - 5 \)[/tex] is [tex]\( -12 \)[/tex].
4. Next, take the absolute value of the inner expression:
[tex]\[
| -12 | = 12
\][/tex]
5. Finally, subtract this absolute value from 8:
[tex]\[
8 - 12 = -4
\][/tex]
So, the value of the expression [tex]\( 8 - |2g - 5| \)[/tex] when [tex]\( g = -3.5 \)[/tex] is [tex]\( -4 \)[/tex].
Thus, the correct answer is:
D. [tex]\(-4\)[/tex]
