Answer
{$x | x \lt- 1$}
Work Step by Step
This set includes from negative infinity up to but not including one. This means that $x$ can be anything "less than" one, or $x \lt -1$.
When indicating this on a number line, you start with an open point at one to show it is not included, and then shade towards the negative end of the number line, and put an arrow at the end to show it continues to negative infinity.