Question

Use the image to answer the question.



Weston solved an inequality and graphed the solution on the number line. Which of the following inequalities did he solve?

(1 point)
Responses

m + 0.5 ≥ 0.5
m + 0.5 ≥ 0.5

m + 5 ≥ 6
m + 5 ≥ 6

m − 0.5 ≤ 0.5
m − 0.5 ≤ 0.5

m − 1 > 0

Answer 1

To determine which inequality Weston solved based on the graph you mentioned, we would need to interpret how the solution is presented on the number line. Typically, a number line graph will indicate whether the interval includes endpoints (closed dot for ≥ or ≤) or not (open dot for > or <), and whether the interval extends toward positive or negative infinity.

Here's a brief analysis of each option:

1. **m + 0.5 ≥ 0.5**: This simplifies to m ≥ 0. This would be represented by a closed dot at 0 and shading to the right.

2. **m + 5 ≥ 6**: This simplifies to m ≥ 1. This would be represented by a closed dot at 1 and shading to the right.

3. **m − 0.5 ≤ 0.5**: This simplifies to m ≤ 1. This would be represented by a closed dot at 1 and shading to the left.

4. **m − 1 > 0**: This simplifies to m > 1. This would be represented by an open dot at 1 and shading to the right.

Without the image, we can only analyze these inequalities theoretically. If the graph had a closed dot at 1 and shaded to the left, the answer would be option 3. If the graph had a closed dot at 0 and shaded to the right, option 1 would be correct. For an open dot at 1 and shading to the right, option 4 is the answer, and for a closed dot at 1 and shading to the right, option 2 would be correct.

Please compare the characteristics of the graph with the descriptions above to identify the correct inequality.