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 3.5d:

Answer:

Solution:

Either or

Step 1: Solve

Step 2: Solve

There are four 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 x=2.57603367 by substituting 2.57603367 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 2.57603367 for x, then x=2.57603367 is not a solution.

Check the solution x = - 4.07603367 by substituting -4.07603367 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 -4.07603367 for x, then x=-4.07603367 is a solution.

Check the solution x=2.7413587 by substituting 2.7413587 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 2.7413587 for x, then x=2.7413587 is not a solution.

Check the solution x=-0.8663587 by substituting x=-0.8663587 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 x=-0.8663587 for x, then x=-0.8663587 is 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 two x-intercepts at x=-4.07603367,x=-0.86635871. This verifies the solutions.

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