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.

Problem 3.3b:

Solutions:

Either or

Step 1: Solve

Step 2: Solve

The answers are and x = -1.

Step 3: Check the solution by substituting 0.333333 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 equals the right side of the original equation when 0.333333 is substituted for, then x = 0.333333 is a valid solution.

Check the solution x=-1 by substituting -1 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 equals the right side of the original equation when -1 is substituted for, then x=-1 is a valid solution.

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 -1. This verifies the solutions.

If you would like to review the answer and solution to problem 3.3c, click on solution.

If you would like to go back to the problem page, click on problem.

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