#### 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 3.5b:

Solution:

Either or

Step 1: Solve

Step 2: Solve

There are four real answers:. : However all these answers may or may not be solutions. You must verify that your answers are the solutions to the original equation.

Step 4:Check the solutions:

Check by substituting 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 is not equal to the right side of the original equation after we substitute the value for x, then is not a solution.

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:

Since the left side of the original equation is equal to the right side of the original equation after we substitute the value -2 for x, then x=-2 is a solution.

Check the solution by substituting 2.83205 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 is equal to the right side of the original equation after we substitute the value for x, then is a solution.

Check the solution by substituting x=-0.73205 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: -3.9282

Since the left side of the original equation is not equal to the right side of the original equation after we substitute the value 1- for x, then is not a solution.

There are two solutions:

You can also verify these two real answers by graphing

The graph is formed by subtracting the right side of the original equation from the left side of the original equation. Note that there are x-intercepts at -2 and at 2.73205. This verifies there the two solutions.

If you would like to review the solution to problem 3.5c, click on Solution

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

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