Use the image to answer the question. Preston solved an inequality and graphed the solution on the number line. Which of the following inequalities did he solve?
the line graph starts at -10 and ends at 10, the closed circle is between 1 and 2, the shaded line ends until it hits 10
Answers:
2.1x + 5.6 ≥ 8.75
3.4x - 1.2 ≥ 4.75
Unfortunately, there is a misunderstanding as I'm unable to view images or any visuals provided in this text-based interface.
However, with your description of the graph, we can still determine which inequality corresponds to the solution graphed by Preston. You mentioned that the graph:
- Starts at -10 and ends at 10.
- Has a closed circle between 1 and 2.
- The shaded line continues until it hits 10.
Since there is a closed circle, this indicates that the inequality includes the point where the circle is placed, which is the solution to the equality part of the inequality. Since it's between 1 and 2 and the shaded line continues to the right towards 10, it suggests an inequality with solutions that are greater than or equal to the point where the closed circle is located.
We can use this information to find out which inequality was solved by comparing the solutions of your provided inequalities to the graph description:
1. 2.1x + 5.6 ≥ 8.75
To solve this inequality for x:
2.1x ≥ 8.75 - 5.6
2.1x ≥ 3.15
x ≥ 3.15/2.1
x ≥ 1.5
This inequality suggests that the closed circle would be at x = 1.5 and the shading would continue to the right, which is consistent with your graph description.
2. 3.4x - 1.2 ≥ 4.75
To solve this inequality for x:
3.4x ≥ 4.75 + 1.2
3.4x ≥ 5.95
x ≥ 5.95/3.4
x ≥ 1.75
This inequality indicates that the closed circle would be at x = 1.75 and the shading would continue to the right, which could also be consistent with your graph description since 1.75 is between 1 and 2.
Given the two options and without the exact point for the closed circle, both inequalities seem to fit the description provided. If the closed circle is exactly at 1.5, the first equation is correct. If the circle is closer to 1.75, then the second equation would be correct. Since your description did not provide the exact point, either inequality could potentially match Preston's graph, although the closed circle must be precisely at the solution point to determine the exact inequality he solved.