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Solve 8.2w≤29.52 . Which of the following must be true about the inequality and resulting graph? Select the three that apply.NOTE: There is a check answer button in the bottom right corner. Click this to check your answer before moving on to the next question. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature once per question.(3 points)Responsesw≥3.6w is greater than or equal to 3 point 6The arrow points to the right.The arrow points to the right.w≤3.6w is less than or equal to 3 point 6There is an open circle at 3.6There is an open circle at 3.6There is a closed circle at 3.6There is a closed circle at 3.6The arrow points to the left.

1 answer

To solve the inequality \(8.2w \leq 29.52\), we first isolate \(w\):

  1. Divide both sides by \(8.2\):

\[ w \leq \frac{29.52}{8.2} \]

  1. Calculate \(\frac{29.52}{8.2}\):

\[ \frac{29.52}{8.2} = 3.6 \]

So, the inequality simplifies to:

\[ w \leq 3.6 \]

Now, let's analyze the properties of the inequality and the resulting graph:

  1. w ≤ 3.6: This is true since we derived this inequality.
  2. The arrow points to the left: Since \(w\) is less than or equal to 3.6, the graph will display a leftward arrow starting from 3.6.
  3. There is a closed circle at 3.6: Since the inequality is less than or equal to (≤), the point 3.6 is included in the solution set, hence we use a closed circle.

Let’s summarize the three true statements that must apply:

  1. w ≤ 3.6
  2. The arrow points to the left.
  3. There is a closed circle at 3.6.

The other statements like \(w ≥ 3.6\), “open circle,” and “arrow points to the right” are not valid based on our solution.

So, the correct choices are:

  • \(w \leq 3.6\)
  • The arrow points to the left.
  • There is a closed circle at 3.6.