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Question

Solve Inequalities By Adding or Subtracting Quick Check
2 of 52 of 5 Items
Question
Use the image to answer the question.

A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed circle is plotted on the number line at negative 2. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.

The number line shows the solution of which of the following inequalities?

(1 point)
Responses

9+m≤11
9 plus m less-than-or-equal-to 11

11+m≥9
m plus 9 greater-than-or-equal-to 11

11+m≤9
11 plus m less-than-or-equal to 9

9+m≥11

Answer 1

The number line described shows a closed circle at -2 with a leftward arrow, indicating that the solution includes all numbers less than or equal to -2.

Let's analyze the options given:

1. 9 + m ≤ 11: This simplifies to \( m ≤ 2 \). This does not match the number line.
2. 11 + m ≥ 9: This simplifies to \( m ≥ -2 \). This does not match the number line either.
3. 11 + m ≤ 9: This simplifies to \( m ≤ -2 \). This matches the number line.
4. 9 + m ≥ 11: This simplifies to \( m ≥ 2 \). This does not match the number line.

Based on this analysis, the inequality that corresponds to the number line is:

11 + m ≤ 9.