#### SOLVING EQUATION 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 1:

Either or

Step 1: Solve

Step 2: Solve

There are 4 answers: the approximate answers are and -1.73205080757, and the exact answers are x = - 3 and 1.

Check the solution x = 1.73205080757 by substituting 1.73205080757 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 1.73205080757 for x, then x = 1.73205080757 is a solution.

Check the solution x = - 1.73205080757 by substituting - 1.73205080757 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 - 1.73205080757 for x, then x = - 1.73205080757 is not a solution.

Check the solution x = - 3 by substituting - 3 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 - 3 for x, then x=-3 is a solution.

Check the solution x = 1 by substituting 1 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 1 for x, then x=1 is not a solution.

The solutions are 1.73205080757 and - 3.

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 -3. This means that the two real solutions are 1.73205080757 and -3.

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