To find the value of the expression [tex]\(-3|t-8| + 1.5\)[/tex] when [tex]\(t = 12\)[/tex], follow these steps:
1. Substitute the value of [tex]\(t\)[/tex]:
[tex]\[
t = 12
\][/tex]
The expression becomes:
[tex]\[
-3|12 - 8| + 1.5
\][/tex]
2. Calculate the absolute value:
[tex]\[
12 - 8 = 4
\][/tex]
[tex]\[
|4| = 4
\][/tex]
3. Multiply by -3:
[tex]\[
-3 \times 4 = -12
\][/tex]
4. Add 1.5:
[tex]\[
-12 + 1.5 = -10.5
\][/tex]
So, the value of the expression when [tex]\(t = 12\)[/tex] is:
[tex]\[
-10.5
\][/tex]
Hence, the correct answer is:
[tex]\[
\boxed{-10.5}
\][/tex]
