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 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.

If you would like to work another example, click on Example

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

If you would like to go back to the equation table of contents, click on Contents.

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