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

Answer 1

To determine which inequality Weston solved based on the description of the number line, let's analyze the details provided:

1. The closed circle at 1 indicates that \( x \) can equal 1 (this implies at least a "greater than or equal to" condition).
2. The line drawn from 1 toward 10 (with an arrow at the end) suggests that \( x \) is greater than 1, extending towards positive infinity.

Given this information, the inequality that fits the description is:

\( x - 1 \geq 0 \) or simplified to \( x \geq 1 \).

However, since the options provided do not include exactly this inequality but include \( x - 1 > 0 \) which means \( x > 1 \).

The inequalities you provided are:

• \( x - 1 > 0 \) (this means \( x > 1 \))
• \( x + 5 \geq 6 \) (this simplifies to \( x \geq 1 \), but it's not a direct match to the graph)
• \( x + 0.5 \geq 0.5 \) (this is \( x \geq 0 \))
• \( x - 0.5 \leq 0.5 \) (this simplifies to \( x \leq 1 \))

Based on the reasoning, the most accurate choice corresponding with the graph is:

\( x - 1 > 0 \) (which means \( x > 1 \)).