Solved on Dec 15, 2023

Graph the interval {xRx>8}\{x \in \mathbb{R} | x > 8\} on the number line.

STEP 1

Assumptions
1. We are working with a real number line.
2. The inequality given is 8<x8 < x, which means we are looking for all real numbers greater than 8.
3. The interval will be open since the inequality does not include the number 8 (it is not 8x8 \leq x).

STEP 2

Start by drawing a horizontal line to represent the number line. Mark the point corresponding to the number 8.

STEP 3

Since the inequality is 8<x8 < x, we want to indicate that all numbers greater than 8 are part of the solution. To do this, draw an open circle (or a small unfilled circle) at the point corresponding to 8 to show that 8 is not included in the interval.

STEP 4

Draw an arrow starting from the open circle at 8 and extending to the right, indicating that all numbers to the right of 8 are included in the solution set.

STEP 5

Label the number line with appropriate numbers to give context to the location of the number 8 and the direction of the arrow.
The graph of the interval 8<x8 < x on the number line has been completed. It shows all numbers greater than 8, extending to infinity to the right, with an open circle at 8 indicating that 8 itself is not included in the interval.

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