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

The number line you described has a point at \(4 \frac{1}{4}\) (which is equivalent to \(4.25\)) with an arrow going to the right. This indicates that the values of \(x\) are greater than \(4 \frac{1}{4}\).

To express this as a linear inequality with \(x\) coming first, it would be written as:

\[ x > 4 \frac{1}{4} \]

In decimal form, this can also be written as:

\[ x > 4.25 \]

So, the inequality representing the graph is either \(x > 4 \frac{1}{4}\) or \(x > 4.25\).

I apologize for the confusion. Based on your description, if the arrow is pointing to the right from \(4 \frac{1}{4}\) (4.25), it indicates that the values of \(x\) are greater than or equal to \(4 \frac{1}{4}\).

In that case, the correct inequality should be:

\[ x \geq 4 \frac{1}{4} \]

In decimal form, it can also be expressed as:

\[ x \geq 4.25 \]

Thank you for your patience, and I'm here to assist you further if needed!