Question

linear equations and inequalities
set-builder and interval notation
graph the set \\{x \mid x > 0\\} on the number line.
then, write the set using interval notation.
\\{x \mid x > 0\\} =
(there are some interface elements like number line drawing tools and interval notation input options in the image, but the main problem text is as above)

Explanation:

Step1: Analyze the inequality

The set is \(\{x \mid x > 0\}\), which means all real numbers greater than 0.

Step2: Determine interval notation

For \(x > 0\), the interval starts at 0 (not including 0, so we use a parenthesis) and goes to positive infinity (also using a parenthesis as infinity is not a real number to be included). So the interval notation is \((0, \infty)\).

Step3: Graph on number line

On the number line, we place an open circle at 0 (since 0 is not included in the set) and draw an arrow to the right (indicating all numbers greater than 0).

Answer:

The interval notation for \(\{x \mid x > 0\}\) is \((0, \infty)\). For the graph, there is an open circle at 0 and an arrow pointing to the right along the number line.