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Use the image to answer the 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−1>0
x minus 1 greater-than 0

x+5≥6

1 answer

To determine which inequality Weston solved based on the graph, we need to analyze the given details:

  • The closed circle at 1 indicates that 1 is included in the solution (meaning the inequality is either greater than or equal to or less than or equal to).
  • The arrow extending from 1 to the right towards 10 indicates that the solution includes all numbers greater than 1.

Given this interpretation, we can examine the provided inequalities:

  1. x + 0.5 ≥ 0.5: This rearranges to x ≥ 0. The solution includes 0 and all values to the right, which does not align with the graph.

  2. x - 0.5 ≤ 0.5: This rearranges to x ≤ 1. This suggests points less than or equal to 1, which does not match the graph.

  3. x - 1 > 0: This rearranges to x > 1. This means all numbers greater than 1, which aligns with the graph indicating values greater than 1 with a closed circle on 1.

  4. x + 5 ≥ 6: This rearranges to x ≥ 1. This means all numbers greater than or equal to 1, which also aligns, but it does not match the arrow only going toward numbers greater than 1.

Since the graph shows a closed circle on 1 and an arrow pointing to the right, the most fitting inequality that Weston solved is:

x - 1 > 0 (x > 1).