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 3.3c:

Answer: and

Solutions:

Either or

Step 1: Solve

Step 2: Solve

The answers are (rounded) and *(rounded)

Step 3: Check the solution by substituting -1.26087 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 -1.26087 is substituted for, then x=-1.26087 is a valid solution.

Check the solution by substituting -0.67568 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 -0.67568 is substituted for, then x=-0.67568 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 This verifies the solutions.

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

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

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

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