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−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 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
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Answer 1

To determine which inequality Weston solved based on the description of the number line, we need to analyze the information given:

1. The number line indicates a closed circle at 1, which means that the solution includes the value of 1.
2. The arrow extends towards 10, implying that the values greater than 1 are included in the solution.

This means the solution set is \( x \geq 1 \).

Now, let's analyze the provided inequalities:

1. \( x - 1 > 0 \): This simplifies to \( x > 1 \). This does not include 1, so it does not match the description.

2. \( x + 5 \geq 6 \): This simplifies to \( x \geq 1 \). This does match the description, as it includes 1 and all values greater than 1.

3. \( x - 0.5 \leq 0.5 \): This simplifies to \( x \leq 1 \). This does not match the description as it does not include values greater than 1.

4. \( x + 0.5 \geq 0.5 \): This simplifies to \( x \geq 0 \). While this includes 1, it also includes values less than 1, which does not match the specific condition of the graph.

Based on the analysis, the correct inequality that Weston solved is:

\( x + 5 \geq 6 \).