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+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

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

x−1>0

Answer 1

The graph described indicates that Weston solved an inequality that includes the number 1 and continues toward 10 with a closed circle, which denotes that 1 is included in the solution set.

Let's analyze the given options with this in mind:

1. x + 0.5 ≥ 0.5: This would result in x ≥ 0, which includes x values starting at 0, not 1.

2. x - 0.5 ≤ 0.5: This simplifies to x ≤ 1. This would result in an open circle at 1, not a closed one as described.

3. x + 5 ≥ 6: This simplifies to x ≥ 1. This describes a closed circle at 1 and includes all numbers greater than or equal to 1. This matches the description given.

4. x - 1 > 0: This simplifies to x > 1, which would result in an open circle at 1, not a closed one.

Based on the provided graph and analysis, the inequality Weston solved is:

x + 5 ≥ 6.