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Simplifying Multiple Positive or Negative Signs

Examine the first example problem.

16 - - 4 = 5x

Again, the equation above has two negative signs. Each negative sign indicates a negation or opposite. Think of the problem this way: You start out adding 16 and 4 but the first negative sign indicates that subtraction should be used instead of addition (the opposite operation). Then the second negative indicates another opposite -- that is, addition should be used instead of subtraction.

Since after considering all of the negative signs, addition is the current operation, the problem can be rewritten as:

16 + 4 = 5x

The problem below is a slight variation from the last one we worked on. This problem is similar in that it has two negative signs between the 16 and 4 but now it also has a + sign.

16 - + - 4 = 5x

The only new thing you need to know to simplify this problem is that unlike a negative sign, the plus sign or positive sign does not change the operation. Keeping this in mind we will simplify the equation.

We start out adding the 16 and 4 until we see the first negative sign, so we change the operation to subtract. The next sign is a plus sign, so we continue to subtract. The last sign is a negative sign, so again we do the opposite and add. Now we can rewrite the problem, replacing the old signs with a single plus sign.

16 + 4 = 5x

Using these simple rules you can easily simplify multiple signs.

In practice, and in our worksheets, you will not generally encounter more than two positive or negative signs together. Also, multiple negative signs are often separated using parentheses for sake of clarity.

10 - (-5)
has the same meaning as 10 - - 5.

The next page will link to a list of resources including practice problems and additional lessons in simplifying.


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