To determine the value of the expression [tex]\(-3|t-8| + 1.5\)[/tex] when [tex]\( t = -12 \)[/tex], let’s break it down step by step.
1. Substitute the value of [tex]\( t \)[/tex] into the expression inside the absolute value:
[tex]\[
t - 8 = -12 - 8 = -20
\][/tex]
Hence, the value inside the absolute value operator is [tex]\(-20\)[/tex].
2. Determine the absolute value:
[tex]\[
|t - 8| = |-20| = 20
\][/tex]
3. Substitute [tex]\( |t - 8| \)[/tex] into the expression:
[tex]\[
-3|t-8| + 1.5 = -3 \cdot 20 + 1.5
\][/tex]
4. Perform the multiplication and addition:
[tex]\[
-3 \cdot 20 = -60
\][/tex]
[tex]\[
-60 + 1.5 = -58.5
\][/tex]
So, the value of the expression when [tex]\( t = -12 \)[/tex] is [tex]\(-58.5\)[/tex].
Thus, the correct answer is:
D. [tex]\(-58.5\)[/tex]
