Question

plot the solution for the range of acceptable suitcase weights on the number line. use the drawing tool(s) to form the correct answers on the provided number line.
part d
now that youve found the acceptable range of weights for the suitcase, consider the unacceptable weights.
write an inequality you could use to find the range of unacceptable weights for your suitcase, where x is the weight of the suitcase.
drag each term to the correct location on the image.
part e
which inequality describes the unacceptable weights for the suitcase?
options: x < 32.5 or x < 47.5; 32.5 > x > 47.5; x < 32.5 or x > 47.5; 32.5 < x < 47.5

Explanation:

Step1: Identify acceptable weight range

First, we infer the acceptable suitcase weight range is between 32.5 and 47.5 (from the context of the number line and multiple-choice options). This means acceptable weights follow $32.5 < x < 47.5$.

Step2: Define unacceptable weights

Unacceptable weights are all values outside the acceptable range: weights less than 32.5, or weights greater than 47.5.

Step3: Match to correct option

Compare to the given multiple-choice options to find the matching inequality.

Step1: Set up absolute value inequality

The acceptable range is $|x - 40| < 7.5$, so unacceptable weights are $|x - 40| > 7.5$.

Step2: Drag terms to form inequality

Fill the boxes with the corresponding terms:

1. First box: $x - 40$
2. Middle symbol: $>$
3. Last box: $7.5$

Step1: Mark open points

Place open points at $32.5$ and $47.5$ on the number line.

Step2: Draw rays for unacceptable range

Draw a ray pointing left from the open point at $32.5$, and a ray pointing right from the open point at $47.5$.

Answer:

x < 32.5 or x > 47.5

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For the drag-and-drop (Part D):