#### 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.

• Step 4:Check your answer analytically or graphically.

Solve for x in the following equation.

Example 2: Step 1:The absolute value is already isolated.

Since and , 5x+7=3 or 5x+7=-3

Step 2:Set the quantity within the absolute value notation to  Step 3:Solve for x in the equation 5x+7=3 Solve for x in the equation 5x+7=-3. The answers are and -2.

Step 4: Check the solutions because answers are not always valid solutions to the equation.

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: Since the left side of the original equation after we substituted the value for, the solution is valid

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: Since the left side of the original equation after we substituted the value -2 for, the solution x=-2 is valid

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 -2. this verifies our solutions graphically.

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