#### 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 3:

Either or

Step 1: Solve

Step 2: Solve

There are four real answers at -0.683959382319, 10.1564005278, and -0.65640052777. However all these answers may or may not be solutions. You must verify that your answers are the solutions to the original equation.

Step 4:Check the solutions:

Check by substituting 12.1839593823 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 12.1839593823 for x, then is a solution.

Check the solution by substituting -0.683959382319 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 -0.683959382319 for x, then is a solution.

Check the solution by substituting 10.1564005278 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 10.1564005278 for x, then is not a solution.

Check the solution by substituting -0.65640052777 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 -0.65640052777 for x, then is not a solution.

The solutions are

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 and -0.6839593823. This verifies that the solutions are and -0.6839593823.

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

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