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 3.5a:

Answer:

Either or

Step 1: Solve

Step 2: Solve

There are four answers: 0.115562689514, and 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 2.88443731049 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 2.88443731049 for x, then is a solution.

Check the solution by substituting 0.115562689514 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: 0.346688068

• 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 0.115562689514 for x, then is a solution.

Check the solution 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 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.

The solutions are and 0.1155626895142.

You can also check your 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 the graph has two x-intercepts located at and 0.1155626895142 This verifies the two real solutions.

If you would like to review the solution to problem 3.5b, 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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