Solve 8.2w≤29.52

Question

. Which of the following must be true about the inequality and resulting graph? Select the three that apply.

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(3 points)
Responses

There is an open circle at 3.6
There is an open circle at 3.6

w≤3.6
w is less than or equal to 3 point 6

w≥3.6
w is greater than or equal to 3 point 6

The arrow points to the right.
The arrow points to the right.

There is a closed circle at 3.6
There is a closed circle at 3.6

The arrow points to the left.

Answer 1

To solve the inequality \( 8.2w \leq 29.52 \), we can start by isolating \( w \):

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

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

Calculating \( \frac{29.52}{8.2} \):

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

So we have:

\[ w \leq 3.6 \]

Now let's analyze the inequality and the resulting graph:

1. There is an open circle at 3.6: False. The inequality is "less than or equal to," so we use a closed circle.

2. w ≤ 3.6: True. This is exactly what we found.

3. w ≥ 3.6: False. The inequality indicates that \( w \) is less than or equal to 3.6, not greater.

4. The arrow points to the right: False. Since \( w \) can take values less than or equal to 3.6, the arrow points to the left.

5. There is a closed circle at 3.6: True. Because the inequality includes "equal to," we use a closed circle.

6. The arrow points to the left: True. The graph represents the values less than or equal to 3.6, so it points to the left.

The three correct statements are:

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