The coordinates of the points at a distance d units from the point with coordinate a on the number line are the solutions to the equation |x−a|=d.Therefore, the coordinates of the points at a distance of 3 units from the point with coordinate −4 on the number line are the solutions to the equation |x−(−4)|=3, which is equivalent to |x+4|=3. Choice B is incorrect. The solutions of |x − 4| = 3 are the coordinates of the points on the number line at a distance of 3 units from the point with coordinate 4. Choice C is incorrect. The solutions of |x+3|=4 are the coordinates of the points on the number line at a distance of 4 units from the point with coordinate −3. Choice D is incorrect. The solutions of |x−3|=4 are the coordinates of the points on the number line at a distance of 4 units from the point with coordinate 3.