Final answer:
The equation for the surface consisting of all points that are equidistant from the point (-2, 0, 0) and the plane x = 2 is |x - 2| = √((x + 2)^2 + y^2 + z^2).
Step-by-step explanation:
The equation for the surface consisting of all points that are equidistant from the point (-2, 0, 0) and the plane x = 2 can be found using the distance formula. Since the point (-2, 0, 0) is equidistant from the plane x = 2, the distance between any point (x, y, z) on the surface and the point (-2, 0, 0) is equal to the distance between the point (x, y, z) and the plane x = 2.
The distance between a point (x, y, z) and the plane x = 2 can be calculated as |x - 2|. Therefore, the equation for the surface is |x - 2| = √((x + 2)^2 + y^2 + z^2).
For example, if we take a point (4, 3, 1) on the surface, we can check if it satisfies the equation by substituting the values: |4 - 2| = √((4 + 2)^2 + 3^2 + 1^2), which simplifies to 2 = √(36 + 9 + 1), and it is true.