Here's how I think tides work. I'm probably wrong; can you show me where?

I've read a great many explanations about lunar tides, and I'm so dense that none has completely gotten through to me yet. Basically, if the moon is to the right of Earth, I think the water on Earth's right side should be pulled to the right - and the water on Earth's left side should ALSO be pulled to the right, just a little less strongly. So the gravitational explanation for a high tide on the side farthest from the moon doesn't seem right to me.

http://www.29tharmor.com/images/probably-wrong-about-tides.png
Here are some figures showing what I think about tides. There are almost certainly errors in them, but could you please show me exactly where?

2012-07-27T13:00:43Z

Response to first two answers: Thanks. I'll have to read these a few more times; it still seems to me that you're saying that a gravitational pull to the right causes water to bulge to the left, which makes zero sense to me.

connie2012-07-27T12:56:04Z

Favorite Answer

The Moon exerts a stronger attractive force on the water in the near side of the Earth, less on the Earth itself and even less on the water in the far side. Relative to the center of the Earth. They lead to two bulges of water on the Earth's surface. Therefore, we have two high tides per day.
http://www.lcsd.gov.hk/CE/Museum/Space/EducationResource/Universe/framed_e/lecture/ch06/ch06.html (scroll down)

A nice illustration that looks like what you have, I think...
http://www.gly.uga.edu/railsback/Tides/TideBulges.jpeg

EDIT:
All parts of the Earth are subject to the Moon's gravitational forces, causing the water in the oceans to redistribute, forming bulges on the sides near the Moon and far from the Moon. It is NOT the gravitational pull to the right causing water to bulge to the left, but that BOTH SIDES are reacting to the SAME gravitational pull in different ways: one because of being close to the moon, the other because of the inertia winning out over the same gravitational pull.

As gravitational force acts to draw the water closer to the moon, inertia attempts to keep the water in place. But the gravitational force exceeds it and the water is pulled toward the moon, causing a “bulge” of water on the near side toward the moon.

On the opposite side of the Earth, or the “far side,” the gravitational attraction of the moon is less because it is farther away. Here, inertia exceeds the gravitational force, and the water tries to keep going in a straight line, moving away from the Earth, also forming a bulge. In this way the combination of gravity and inertia create two bulges of water.
http://oceanservice.noaa.gov/education/kits/tides/tides03_gravity.html

Howard H2012-07-27T19:37:40Z

The moon's gravity pulls the ocean water nearest to it, pulls the solid earth a bit less, and the ocean on the opposite side even less. So there are 2 tides a day generally, although local conditions can affect this (see Bay of Fundy).

Johnny2012-07-28T01:50:06Z

I can see why this topic is confusing. Ted's edit makes sense. Here's another link:
http://science.jrank.org/pages/6832/Tides-Theories-tidal-action.html