Answer :
To solve the inequality [tex]\(\frac{f}{2} - 9 > 58\)[/tex], we need to determine which of the given values for [tex]\(f\)[/tex] satisfies this condition.
Let's analyze each value step-by-step:
1. For [tex]\(f = 108\)[/tex]:
[tex]\[
\frac{108}{2} - 9 > 58
\][/tex]
[tex]\[
54 - 9 > 58
\][/tex]
[tex]\[
45 > 58 \quad \text{(This is False)}
\][/tex]
2. For [tex]\(f = 106\)[/tex]:
[tex]\[
\frac{106}{2} - 9 > 58
\][/tex]
[tex]\[
53 - 9 > 58
\][/tex]
[tex]\[
44 > 58 \quad \text{(This is False)}
\][/tex]
3. For [tex]\(f = 84\)[/tex]:
[tex]\[
\frac{84}{2} - 9 > 58
\][/tex]
[tex]\[
42 - 9 > 58
\][/tex]
[tex]\[
33 > 58 \quad \text{(This is False)}
\][/tex]
4. For [tex]\(f = 142\)[/tex]:
[tex]\[
\frac{142}{2} - 9 > 58
\][/tex]
[tex]\[
71 - 9 > 58
\][/tex]
[tex]\[
62 > 58 \quad \text{(This is True)}
\][/tex]
Based on the evaluations, the only value of [tex]\(f\)[/tex] that makes the inequality true is [tex]\(f = 142\)[/tex].
Therefore, the solution to the inequality [tex]\(\frac{f}{2} - 9 > 58\)[/tex] is [tex]\(f = 142\)[/tex].
Let's analyze each value step-by-step:
1. For [tex]\(f = 108\)[/tex]:
[tex]\[
\frac{108}{2} - 9 > 58
\][/tex]
[tex]\[
54 - 9 > 58
\][/tex]
[tex]\[
45 > 58 \quad \text{(This is False)}
\][/tex]
2. For [tex]\(f = 106\)[/tex]:
[tex]\[
\frac{106}{2} - 9 > 58
\][/tex]
[tex]\[
53 - 9 > 58
\][/tex]
[tex]\[
44 > 58 \quad \text{(This is False)}
\][/tex]
3. For [tex]\(f = 84\)[/tex]:
[tex]\[
\frac{84}{2} - 9 > 58
\][/tex]
[tex]\[
42 - 9 > 58
\][/tex]
[tex]\[
33 > 58 \quad \text{(This is False)}
\][/tex]
4. For [tex]\(f = 142\)[/tex]:
[tex]\[
\frac{142}{2} - 9 > 58
\][/tex]
[tex]\[
71 - 9 > 58
\][/tex]
[tex]\[
62 > 58 \quad \text{(This is True)}
\][/tex]
Based on the evaluations, the only value of [tex]\(f\)[/tex] that makes the inequality true is [tex]\(f = 142\)[/tex].
Therefore, the solution to the inequality [tex]\(\frac{f}{2} - 9 > 58\)[/tex] is [tex]\(f = 142\)[/tex].
