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

Note:

• if and only if

• if and only if a+b=3 or a+b=-3

• Step 1:Isolate the absolute value expression.

• Step2:Set the quantity inside the absolute value notation equal to + and - the quantity on the other side of the equation.

• Step 3:Solve for the unknown in both equations.

Solve for x in the following equation.

Example 3:

Step 1: The absolute value is already isolated.

Step 2: Set the quantity within the absolute value notation to

or

Step 3: Solve for x in the equation :

Step 4: Solve for x in the equation :

Step 5:Check the solutions.

Check the solution x = 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:

Step 6: Check the solution x = 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:

You can also check your answer by graphing (the left side of the original equation minus the right side of the original equation). You will note that the two x-intercepts on the graph are located at and

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

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