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Use the inequality to answer the question.

−3x+4>−2
Which situation matches the inequality?
Responses
A diver begins at 4 feet above sea level, lowers himself by 3 feet per minute, but needs to stay higher than 2 feet below sea level.

A diver begins at 4 feet above sea level, raises himself by 3 feet per minute, but needs to stay higher than 2 feet below sea level.

A diver begins at 4 feet above sea level, lowers himself by 3 feet per minute, but needs to dive lower than 2 feet below sea level.
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A diver begins at 2 feet below sea level, raises himself by 3 feet per minute, but needs to stay lower than 4 feet above sea level

1 answer

To determine which situation matches the inequality \(-3x + 4 > -2\), we will first rewrite the inequality in a more useful form.

  1. Start with the inequality: \[ -3x + 4 > -2 \]

  2. Subtract 4 from both sides: \[ -3x > -6 \]

  3. Divide both sides by -3 (remember to flip the inequality sign when dividing by a negative number): \[ x < 2 \]

This means \(x\) (the number of minutes the diver has been underwater) must be less than 2.

Now, let's analyze the given scenarios to see which one matches the condition \(x < 2\):

  1. A diver begins at 4 feet above sea level, lowers himself by 3 feet per minute, but needs to stay higher than 2 feet below sea level.

    • This scenario implies that depth increases as time passes, and the current position is given as starting from 4 feet above sea level and moving down. It correlates with a decreasing quantity but does not necessarily require being less than 2.

  2. A diver begins at 4 feet above sea level, raises himself by 3 feet per minute, but needs to stay higher than 2 feet below sea level.

    • This diver is ascending, so this also does not correlate directly with the inequality derived since he starts high and moves higher.

  3. A diver begins at 4 feet above sea level, lowers himself by 3 feet per minute, but needs to dive lower than 2 feet below sea level.

    • This diver is descending. If he starts at 4 and goes down at 3 feet per minute, he would reach 1 foot after 1 minute, and -2 feet after 2 minutes. However, the restriction is to dive lower than -2, which is not aligning with the derived inequality.

  4. A diver begins at 2 feet below sea level, raises himself by 3 feet per minute, but needs to stay lower than 4 feet above sea level.

    • In this case, the diver starts below sea level and is ascending. Since he starts at -2, he could reach sea level in 2 minutes and continues raising himself to below 4, thus possibly satisfying the inequality condition of \(x < 2\).

Based on the analysis, the first scenario most closely matches \(x < 2\):

A diver begins at 4 feet above sea level, lowers himself by 3 feet per minute, but needs to stay higher than 2 feet below sea level.