Simplifying Multiple Positive or Negative Signs Lessons

This is the most basic method for simplifying equations or expressions.

Note: Some instructors choose to cover this topic directly, while others do not. The concepts presented are simple and so we recommend that you follow this lesson so that you will have an understanding of what to do when multiple signs are encountered in the future.

Imagine that you had a conversation with someone and said, "I am not, not hungry." Because you used double negatives, the statement you made would actually mean that you were hungry. This can lead to confusion, and it definately makes the sentence more complex than it needs to be. As a result, the use of double negatives in speech is generally considered improper.

Occasionally you may encounter an algebraic expression or equation that has more than one sign between two terms. If there are two or more negative or subtract signs, then the expression or equation should be simplified.

16 - - 4 = 5x

Using just a few simple to remember rules, multiple signs can be simplified easily.

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.

Simplifying Multiple Signs Resources

Equation Practice Problems / Worksheet
Equations that require simplifying multiple signs before they can be solved.

Equation Calculator
Automatically simplifies multiple signs, then solves the equation.

Simplifying Expressions Calculator
Automatically simplifies multiple signs, in a given expression.

Next Lesson: Combining Like Terms
Compacting equations and expressions by combining like terms.


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