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Addition/Subtraction Class

In the second step, the equation goes from

$$2x-7=15$$

to

$$2x=15+7$$

This suggests a pattern of moving symbols, which has the same effect as the normal method of adding 7 to each side. The visual logic is

1. The -7 is moved from one side of the equation to the opposite side, and
2. its sign is flipped - that is, changed to its opposite. It goes from -7 to +7.

Let's see how you can apply this pattern, using symbol motion. Visualize this equation, like you practiced before:

Next, chunk the -7 - put your attention on the '-7' as a separate object, floating in the containing equation.

Notice that we are taking two symbols here, the - and the 7, and grouping them together in a single chunk. Next, move that chunk:

While the -7 is in motion, flip (change) its sign:

When the motion completes, so does the arithmetic operation:

Here is a summary of what we just did:

1. Visualize the equation.
2. Chunk the term (symbol or symbols) you wish to move, including the + or - in front of it. (If there is no + or - there, insert a + in front of it.)
3. In the image you are visualizing, begin to move the chunk to the opposite side. As you do this, flip the sign inside of the chunk. If it has a + in front, replace that with a -, and vice versa.
4. Move the chunk into the opposite side of the equation. Tack it onto the far right. (You can also add it in between other terms that are being added or subtracted. If you put it on the far left, place a + sign between it and the next term.)

You can verify that you moved the symbols correctly, by doing the equivalent operation the ``normal'' way - by adding or subtracting an expression on each side - and check whether the answer is the same.