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 3.3d:

Answer: -2.19316, 0.666667, and -0.833333

Either or

Step 1: Solve the equation

Step 2: Solve the equation

The answers are 2.026498, -2.1931648, 0.666667 and -0.833333.

Step 3: Check the solution x = 2.026498 by substituting 2.026498 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 2.026498 for, the solution x = 2.026498 is valid

Check the solution x = -2.1931648 by substituting -2.1931648 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 -2.1931648 for, the solution x = -2.1931648 is valid.

Check the solution x = 0.666667 by substituting 0.666667 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 0.666667 for, the solution x = 0.666667 is valid.

Check the solution x = -0.833333 by substituting -0.833333 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 -0.833333 for, the solution x = -0.833333 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 four x-intercepts on the graph are located at x = 2.026498, -2.1931648, 0.666667 and -0.833333. This verifies our answers.

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