#### SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:

• if and only if

• if and only if a+b=3 or a+b=-3

• if any only if a+b=+(x+y) or a+b=-(x+y)

Solve for x in the following equation.

Example 2:

Either or

Step 1: Solve

Step 2: Solve

There are two real answers at and 0.219223593596,

and two imaginary answers at and

Check the solution by substituting 2.2807764064 in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.

• Left Side:

• Right Side:

Since the left side of the original equation is equal to the right side of the original equation after we substitute the value 2.2807764064 for x, then is a solution.

Check the solution by substituting 0.219223593596 in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.

• Left Side:

• Right Side:

Since the left side of the original equation is equal to the right side of the original equation after we substitute the value 0.219223593596 for x, then is a solution.

Check the solution by substituting in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.

• Left Side:

• Right Side:

Since the left side of the original equation is not equal to the right side of the original equation after we substitute
the value for x, then is not a solution.

Check the solution by substituting in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.

• Left Side:

• Right Side:

Since the left side of the original equation is not equal to the right side of the original

equation after we substitute the value for x, then is not a solution.

The solutions are 1.73205080757 and -3.

You can also check the real answers by graphing

The graph is formed by subtracting the right side of the original equation from the left side of the original equation. Note that the graph has two x-intercepts located at 1.73205080757 and 1-3. This means that the two real solutions are 1.73205080757 and -3.

If you would like to work another example, click on Example.

If you would like to test yourself by working some problems similar to this example, click on Problem.

[Algebra] [Trigonometry]
[Geometry] [Differential Equations]
[Calculus] [Complex Variables] [Matrix]
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