9. Solve for   x   and check

x + 7 = 3x - 1

First get the x's together on one side. Since there are more   x's   on the right get rid of the   x   on the left. Since the   x   on the left is added, we will need to subtract   x   from both sides

 x + 7 = 3x - 1 - x - x 7 = 2x - 1

Now we need to get all of the numbers together. If we want our   x's   on the right, then we will want our numbers on the left. To accomplish this we will need to get rid of the -1 on the right side. Add 1 to both sides

 7 = 2x - 1 + 1 + 1 8 = 2x

Now divide both sides by 2

8/2 = 2x/2

4 = x
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There is a shortcut. We can subtract   x   in the following way

 x + 7 = 3x - 1 7 = 3x - 1 - x

The reason we are subtracting   x   from both sides is to get rid of the   x   on the left side of the equation. If we do whatever it takes to get rid of the   x   on the left, then the   x   will be gone from the left. We can simply express this by getting rid of it.

Next we are going to get rid of the -1 on the right. To do this we add 1 to both sides. The result looks like

7 = 3x - 1 - x

1 + 7 = 3x - x

This can be done in one step

x + 7 = 3x - 1

1 + 7 = 3x - x

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This process is called transposing terms. When you get rid of a term on one side of an equation it pops up on the other side with a different sign. This gets us to the step

8 = 2x

Now divide both sides by 2

8/2 = 2x/2

4 = x

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Check

(4) + 7 = 3(4) - 1

4 + 7 = 12 - 1

11 = 11