#### 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 1: Step 1:The absolute value is already isolated.

Either 2x-1=+5 or 2x-1=-5

Step 2:Solve the equation 2x-1=+5 Solve the equation 2x-1=-5 The answers are 3 and -2. These answers may not be solutions to the equation.

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: Check the solution x = -2 by substituting -2 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: The solutions are x=3 and -2.

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 3 and -2. This verifies our solutions graphically.

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