Let's solve the inequality step-by-step and determine which of the given options are elements of the solution set.
1. We start with the inequality:
[tex]\[
x - 72 \geq -96
\][/tex]
2. To isolate [tex]\( x \)[/tex], we need to add 72 to both sides of the inequality:
[tex]\[
x - 72 + 72 \geq -96 + 72
\][/tex]
3. Simplifying both sides, we get:
[tex]\[
x \geq -24
\][/tex]
So, the inequality simplifies to [tex]\( x \geq -24 \)[/tex]. We now test each option against this condition to see if it satisfies the inequality.
- Option A: 14
[tex]\[
14 \geq -24 \quad \text{(True)}
\][/tex]
- Option B: -28
[tex]\[
-28 \geq -24 \quad \text{(False)}
\][/tex]
- Option C: -80
[tex]\[
-80 \geq -24 \quad \text{(False)}
\][/tex]
- Option D: -24
[tex]\[
-24 \geq -24 \quad \text{(True)}
\][/tex]
- Option E: -25
[tex]\[
-25 \geq -24 \quad \text{(False)}
\][/tex]
- Option F: 23
[tex]\[
23 \geq -24 \quad \text{(True)}
\][/tex]
Thus, the values that satisfy the inequality [tex]\( x \geq -24 \)[/tex] are 14, -24, and 23.
Therefore, the answers that are elements of the solution set of the inequality [tex]\( x - 72 \geq -96 \)[/tex] are:
A. 14
D. -24
F. 23
