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Which of the following are solutions to the inequality below? Select all that apply.

[tex]\[ 13 > -2 + \frac{f}{4} \][/tex]

A. [tex]\( f = 4 \)[/tex]
B. [tex]\( f = 44 \)[/tex]
C. [tex]\( f = -108 \)[/tex]
D. [tex]\( f = -104 \)[/tex]

Answer :

To determine which of the given values of [tex]\( f \)[/tex] satisfy the inequality [tex]\( 13 > -2 + \frac{f}{4} \)[/tex], let’s check each value step-by-step:

1. For [tex]\( f = 4 \)[/tex]:
[tex]\[
13 > -2 + \frac{4}{4}
\][/tex]
Simplify [tex]\( \frac{4}{4} \)[/tex]:
[tex]\[
13 > -2 + 1
\][/tex]
Simplify the right side:
[tex]\[
13 > -1
\][/tex]
This statement is true.

2. For [tex]\( f = 44 \)[/tex]:
[tex]\[
13 > -2 + \frac{44}{4}
\][/tex]
Simplify [tex]\( \frac{44}{4} \)[/tex]:
[tex]\[
13 > -2 + 11
\][/tex]
Simplify the right side:
[tex]\[
13 > 9
\][/tex]
This statement is also true.

3. For [tex]\( f = -108 \)[/tex]:
[tex]\[
13 > -2 + \frac{-108}{4}
\][/tex]
Simplify [tex]\( \frac{-108}{4} \)[/tex]:
[tex]\[
13 > -2 - 27
\][/tex]
Simplify the right side:
[tex]\[
13 > -29
\][/tex]
This statement is true as well.

4. For [tex]\( f = -104 \)[/tex]:
[tex]\[
13 > -2 + \frac{-104}{4}
\][/tex]
Simplify [tex]\( \frac{-104}{4} \)[/tex]:
[tex]\[
13 > -2 - 26
\][/tex]
Simplify the right side:
[tex]\[
13 > -28
\][/tex]
This statement is true too.

Given all these checks, the values of [tex]\( f \)[/tex] that satisfy the inequality [tex]\( 13 > -2 + \frac{f}{4} \)[/tex] are:
- [tex]\( f = 4 \)[/tex]
- [tex]\( f = 44 \)[/tex]
- [tex]\( f = -108 \)[/tex]
- [tex]\( f = -104 \)[/tex]

So, all the given values of [tex]\( f \)[/tex] are solutions to the inequality.

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