Answer
$[1, +\infty)$
Refer to the graph below.
Work Step by Step
The conjunction "or" means union.
Recall:
The union of sets $A$ and $B$, denoted by $A\cup B$, is the set that contains the combined elements of $A$ and $B$.
$x\ge1$ includes all real numbers greater than or equal to $1$.
In interval notation, the set is $[1, +\infty).$
$x\ge8$ includes all real numbers greater than or equal to $8$.
In interval notation, the set is $[8, +\infty).$
Thus, the union of the two given sets is $[1, +\infty) \cup [8, +\infty)$, which when simplified becomes $[1, +\infty)$.
To graph this solution set, plot a solid dot at $1$ then shade the region to its right.
Refer to the graph above.