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Answer :
We start by expressing the diver’s elevation after [tex]$x$[/tex] minutes. Since she begins at an elevation of [tex]$-25$[/tex] feet and she descends at [tex]$10$[/tex] feet per minute (note the descent means the rate is added as [tex]$-10$[/tex]), her elevation after [tex]$x$[/tex] minutes can be written as:
[tex]$$-25 - 10x.$$[/tex]
The condition “deeper than [tex]$-220$[/tex] feet” means that her elevation is less than [tex]$-220$[/tex] feet. This gives us the inequality:
[tex]$$-25 - 10x < -220.$$[/tex]
Now, let’s solve this inequality step by step:
1. Add 25 to both sides:
[tex]$$-25 - 10x + 25 < -220 + 25$$[/tex]
[tex]$$-10x < -195.$$[/tex]
2. Divide both sides by [tex]$-10$[/tex]:
When dividing by a negative number, the inequality sign must be reversed:
[tex]$$x > \frac{-195}{-10}.$$[/tex]
Simplifying the division, we get:
[tex]$$x > 19.5.$$[/tex]
So, it will take more than [tex]$19.5$[/tex] minutes for the diver to reach an elevation deeper than [tex]$-220$[/tex] feet.
The inequality that correctly represents the scenario before solving for [tex]$x$[/tex] is:
[tex]$$-25 - 10x < -220.$$[/tex]
This corresponds to option C.
[tex]$$-25 - 10x.$$[/tex]
The condition “deeper than [tex]$-220$[/tex] feet” means that her elevation is less than [tex]$-220$[/tex] feet. This gives us the inequality:
[tex]$$-25 - 10x < -220.$$[/tex]
Now, let’s solve this inequality step by step:
1. Add 25 to both sides:
[tex]$$-25 - 10x + 25 < -220 + 25$$[/tex]
[tex]$$-10x < -195.$$[/tex]
2. Divide both sides by [tex]$-10$[/tex]:
When dividing by a negative number, the inequality sign must be reversed:
[tex]$$x > \frac{-195}{-10}.$$[/tex]
Simplifying the division, we get:
[tex]$$x > 19.5.$$[/tex]
So, it will take more than [tex]$19.5$[/tex] minutes for the diver to reach an elevation deeper than [tex]$-220$[/tex] feet.
The inequality that correctly represents the scenario before solving for [tex]$x$[/tex] is:
[tex]$$-25 - 10x < -220.$$[/tex]
This corresponds to option C.
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