High School

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

\[ 69 < 7 + \frac{f}{2} \]

A. \[ f = 12 \]

B. \[ f = 140 \]

C. \[ f = 136 \]

D. \[ f = 84 \]

Answer :

To solve the inequality [tex]\( 69 < 7 + \frac{f}{2} \)[/tex] and determine which values from the list satisfy this inequality, we'll check each provided value of [tex]\( f \)[/tex].

The inequality can be rewritten in simpler terms:

1. Start with the inequality:
[tex]\[ 69 < 7 + \frac{f}{2} \][/tex]

2. Subtract 7 from both sides to isolate [tex]\(\frac{f}{2}\)[/tex]:
[tex]\[ 69 - 7 < \frac{f}{2} \][/tex]

3. Simplify the left side:
[tex]\[ 62 < \frac{f}{2} \][/tex]

4. Multiply both sides by 2 to solve for [tex]\( f \)[/tex]:
[tex]\[ 124 < f \][/tex]

Now, let's check each value of [tex]\( f \)[/tex] to see if it is greater than 124:

- [tex]\( f = 12 \)[/tex]:
[tex]\( 12 \)[/tex] is not greater than [tex]\( 124 \)[/tex], so it is not a solution.

- [tex]\( f = 140 \)[/tex]:
[tex]\( 140 \)[/tex] is greater than [tex]\( 124 \)[/tex], so it is a solution.

- [tex]\( f = 136 \)[/tex]:
[tex]\( 136 \)[/tex] is greater than [tex]\( 124 \)[/tex], so it is a solution.

- [tex]\( f = 84 \)[/tex]:
[tex]\( 84 \)[/tex] is not greater than [tex]\( 124 \)[/tex], so it is not a solution.

Thus, the values that satisfy the inequality are [tex]\( f = 140 \)[/tex] and [tex]\( f = 136 \)[/tex].

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