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 determine which inequality matches the given description of the number line graph, we need to analyze the graph details:

• The closed circle at 1 indicates that 1 is included in the solution set (i.e., solutions of the inequality at x = 1 are valid).
• The arrow extending to the right toward 10 indicates that all values greater than or equal to the point where the closed circle is located are included in the solution.

This means the solution represents values starting from 1 and going to positive infinity.

Given the options provided:

1. \( x - 1 > 0 \) indicates \( x > 1 \) (not included, doesn't match).
2. \( x + 5 ≥ 6 \) simplifies to \( x ≥ 1 \) (included, matches).
3. \( x + 0.5 ≥ 0.5 \) simplifies to \( x ≥ 0 \) (included, but starting from 0, doesn't match).
4. \( x - 0.5 ≤ 0.5 \) simplifies to \( x ≤ 1 \) (not matching graph).

The inequality that matches the graph, where the solution includes 1 and goes to positive infinity, is:

\( x + 5 ≥ 6 \)