Question

Question

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 minus 0.5 less-than-or-equal-to 0.5

x+0.5≥0.5
x plus 0.5 greater-than-or-equal-to 0.5

x−1>0
x minus 1 greater-than 0

x+5≥6

Answer 1

To determine which inequality Weston solved, we need to interpret the graph on the number line you described. The closed circle on 1 indicates that 1 is included in the solution set, and the line extending toward 10 with an arrow indicates that all numbers greater than or equal to 1 are included in the solution.

This corresponds to the inequality:

x ≥ 1

Now let's examine the given options:

1. x - 0.5 ≤ 0.5

   • Solving for x: x ≤ 1. This would be represented by a closed circle at 1, shading to the left towards negative infinity, which does not match the graph.

2. x + 0.5 ≥ 0.5

   • Solving for x: x ≥ 0. This would not match since the graph includes values starting from 1.

3. x - 1 > 0

   • Solving for x: x > 1. This would be represented by an open circle at 1 and shading to the right, which does not match because the circle is closed.

4. x + 5 ≥ 6

   • Solving for x: x ≥ 1. This is correct and matches the shaded area starting at 1.

Based on the options provided and the description of the graph, the inequality Weston solved is:

x + 5 ≥ 6.