Let's determine which value in the solution set [tex]\( S = \{-16, -2, 2, 4\} \)[/tex] will make the equation true for [tex]\( 5f - 14 = 4f - 16 \)[/tex].
### Step-by-Step Solution
1. Given Equation:
[tex]\[
5f - 14 = 4f - 16
\][/tex]
2. Isolate f:
- Subtract [tex]\( 4f \)[/tex] from both sides:
[tex]\[
5f - 14 - 4f = 4f - 16 - 4f
\][/tex]
Simplifying this gives:
[tex]\[
f - 14 = -16
\][/tex]
- Add 14 to both sides:
[tex]\[
f - 14 + 14 = -16 + 14
\][/tex]
Simplifying this gives:
[tex]\[
f = -2
\][/tex]
3. Check if the value of [tex]\( f \)[/tex] is in the provided solution set [tex]\( S \)[/tex]:
[tex]\[
S = \{-16, -2, 2, 4\}
\][/tex]
The value [tex]\( f = -2 \)[/tex] is indeed in the set [tex]\( S \)[/tex].
### Conclusion
The value from the solution set that makes the equation [tex]\( 5f - 14 = 4f - 16 \)[/tex] true is:
[tex]\[
\boxed{-2}
\][/tex]
