Use the image to answer the question.

Question

A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line between 4 and 5, just after 4. A rightward arrow is marked on the number line that originates at the closed point and goes beyond 10.

What linear inequality is shown graphed on the number line? Make sure to write your inequality so that x comes first.

Answer 1

The closed point plotted between 4 and 5 indicates that the value is included in the solution set, which suggests the inequality is non-strict (includes the endpoint). The rightward arrow extending beyond 10 indicates that x can take any value greater than or equal to the closed point.

Given that the closed point is just after 4, we can denote it as \( x = 4 \) (specifically, we can assume it approaches but does not cross into 5). Therefore, the inequality is:

\[ x \geq 4 \]

So, the linear inequality graphed on the number line is \( x \geq 4 \).

Answer 2

wrong

Answer 3

I apologize for the misunderstanding. Let me clarify the situation and provide the correct answer.

From your description, it seems that the closed point is plotted to the right of 4 and just before 5 on the number line. This means that the point represents a value that is starting from 4 and extending to the right indefinitely.

Since a closed point indicates that the endpoint is included, we would write the inequality to reflect that:

\[ x > 4 \]

However, there was an emphasis on not confusing the situation when I initially interpreted it. If the plot indicates that it is approaching but not quite at 5, and moving rightward, then the inequality does remain as such.

Therefore, if x indeed can take any value greater than 4 but less than or equal to 10, the inequality would actually be:

\[ x \geq 4 \quad \text{and} \quad x < 5 \]

Still, the part where it points rightward suggests it continues beyond 5.

Please confirm:

If the point is closed at 4 and pointing rightwards without indicating an upper limit, the simplified inequality remains:

\[ x \geq 4 \]

If you have specific indications from the image I am missing, please clarify, and I'll correct it accordingly!