Question

Solve 14.8w≤50.32 . 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)ResponsesThere is a closed circle at 3.4There is a closed circle at 3.4w≥3.4w is greater than or equal to 3 point 4The arrow points to the right.The arrow points to the right.The arrow points to the left.The arrow points to the left.w≤3.4w is less than or equal to 3 point 4There is an open circle at 3.4

Answer 1

Let's first solve the inequality \( 14.8w \leq 50.32 \).

1. Divide both sides by 14.8: \[ w \leq \frac{50.32}{14.8} \]

2. Calculate \( \frac{50.32}{14.8} \): \[ w \leq 3.4 \]

The solution to the inequality is \( w \leq 3.4 \).

Now we can analyze the statements regarding the graph of this inequality:

1. There is a closed circle at 3.4: This statement is true because the inequality includes \( 3.4 \) (since it includes equal to, \( \leq \)).

2. w ≥ 3.4: This statement is false. The inequality shows \( w \) is less than or equal to \( 3.4\).

3. The arrow points to the right: This statement is false. The graph will point to the left because \( w \) represents values less than or equal to \( 3.4 \).

4. The arrow points to the left: This statement is true. The graph will point to the left starting from \( 3.4 \).

5. w ≤ 3.4: This statement is true because it accurately represents the solution to the inequality.

6. There is an open circle at 3.4: This statement is false because the circle should be closed (indicating \( w \) can equal \( 3.4 \)).

Based on the analysis, the three statements that must be true are:

1. There is a closed circle at 3.4.
2. The arrow points to the left.
3. w ≤ 3.4.

Make sure to select these three options.