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 4:

Either or

Step 1: Solve the equation

Step 2: Solve the equation

The answers are 2.44832565604 and -1.53165898938.

Step 4: Check the solution x = 2.44832565604 by substituting 2.44832565604 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 2.44832565604 for, the solution x=2.44832565604 is valid

Check the solution x = - 1.53165898938 by substituting -1.53165898938 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 -1.53165898938 for, the solution x = -1.53165898938 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 x = 2.44832565604 and x = -1.53165898938. This verifies our answers.

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

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