$[-1, \infty)$ Refer to the graph below.
Work Step by Step
By subtracting $1$ to both sides we get $$ 1-2x\leq 3 \Longrightarrow 1-2x-1\lt 3-1\Longrightarrow -2x\leq2 .$$ Now, by dividing both sides by $-2$, we have $x\geq -1$. (Note the the inequality symbol will change because a negative number was divided to both sides of the inequality.) In terms of intervals, $x\in [-1,\infty)$. To graph, plot a solid dot at at $x=-1$ then shade the region to its right. See the figure below.