epresent the following sets on a nur a) \( \{x: x \leq 7 ; x \in \mathbb{Z}\} \)

To represent the set \( \{x: x \leq 7 ; x \in \mathbb{Z}\} \) on a number line, you would first identify all integer values that are less than or equal to 7. This includes all integers from negative infinity up to 7, so the set consists of ...,-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7. You would mark the point at 7 with a closed dot to indicate that 7 is included, and shade the line to the left to represent all integers less than 7. Now picture this: if you imagine the number line stretching wide and open, up to infinity on the left and reaching the magical number 7, you'd have a visual party of all those integers, complete with decorations signaling their presence! Just remember: closed dot for included numbers, and open arms for those less than that!!