Use the image to answer the question.

Question

A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. A closed circle is marked on the tick line above 1. A line is drawn from 1 toward 10 with an arrow at the end.

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

(1 point)
Responses

x−1>0
x minus 1 greater-than 0

x+5≥6
x plus 5 greater-than-or-equal-to 6

x+0.5≥0.5
x plus 0.5 greater-than-or-equal-to 0.5

x−0.5≤0.5
x minus 0.5 less-than-or-equal-to 0.5

Answer 1

To analyze the graph described, we have a closed circle at 1 and a line extending towards 10. The closed circle indicates that the value at 1 is included in the solution set, while the arrow pointing to the right indicates that all numbers greater than or equal to 1 are part of the solution.

This means the inequality Weston solved must be read as including the value 1 and extending infinitely toward larger numbers.

Given the options:

1. x − 1 > 0: solution would be x > 1 (not including 1, which is not what we see).

2. x + 5 ≥ 6: when simplified, gives x ≥ 1, which fits the description since it includes 1 and extends right (to infinity). This could be a possible match.

3. x + 0.5 ≥ 0.5: this simplifies to x ≥ 0, which does include values from 0 onward but does not match the description that specifically includes 1 and extends to the right.

4. x − 0.5 ≤ 0.5: simplifies to x ≤ 1, which would lead to a closed circle at 1 but would extend to the left, not matching the graph.

Based on this analysis, the best match for the situation described is:

x + 5 ≥ 6, as it corresponds to the specified graph with the closed circle at 1 and extending rightwards to 10.