To evaluate the expression [tex]\( |2x - 5| \)[/tex] for [tex]\( x = -3 \)[/tex] and [tex]\( x = 3 \)[/tex], let's proceed step-by-step.
### Case 1: [tex]\( x = -3 \)[/tex]
1. Substitute [tex]\( x = -3 \)[/tex] into the expression:
[tex]\[
|2(-3) - 5|
\][/tex]
2. Simplify inside the absolute value:
[tex]\[
2 \cdot (-3) = -6
\][/tex]
[tex]\[
-6 - 5 = -11
\][/tex]
3. Apply the absolute value:
[tex]\[
|-11| = 11
\][/tex]
So, for [tex]\( x = -3 \)[/tex], the value is 11.
### Case 2: [tex]\( x = 3 \)[/tex]
1. Substitute [tex]\( x = 3 \)[/tex] into the expression:
[tex]\[
|2(3) - 5|
\][/tex]
2. Simplify inside the absolute value:
[tex]\[
2 \cdot 3 = 6
\][/tex]
[tex]\[
6 - 5 = 1
\][/tex]
3. Apply the absolute value:
[tex]\[
|1| = 1
\][/tex]
So, for [tex]\( x = 3 \)[/tex], the value is 1.
### Summary
The values of the expression [tex]\( |2x - 5| \)[/tex] for [tex]\( x = -3 \)[/tex] and [tex]\( x = 3 \)[/tex] are:
[tex]\[
11 \text{ and } 1
\][/tex]
Hence, the correct answer is:
D) 11, 1
