Use the image to answer the question.

Question

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

(1 point)
Responses

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

x−1>0
x minus 1 greater-than 0

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 graph of the solution on the number line, we need to evaluate each option:

1. x + 5 ≥ 6

   • Solving this: \( x ≥ 1 \) (shaded to the right starting from 1, including 1).

2. x - 1 > 0

   • Solving this: \( x > 1 \) (shaded to the right starting just after 1, not including 1).

3. x + 0.5 ≥ 0.5

   • Solving this: \( x ≥ 0 \) (shaded to the right starting from 0, including 0).

4. x - 0.5 ≤ 0.5

   • Solving this: \( x ≤ 1 \) (shaded to the left ending at 1, including 1).

Without seeing the actual graph, judging by the type of shading (whether it includes the endpoint or not) will help determine the correct answer.

• If the graph shows a solid dot at 1 and shading to the right, then the answer is x + 5 ≥ 6.
• If the graph shows an open dot at 1 and shading to the right, then the answer is x - 1 > 0.
• If the graph shows a solid dot at 0 and shading to the right, then the answer is x + 0.5 ≥ 0.5.
• If the graph shows a solid dot at 1 and shading to the left, then the answer is x - 0.5 ≤ 0.5.

Please choose the inequality that matches the given graph.