Note:
Problem 3.4b:
Answer:
Isolate the absolute value term.
Either or
Solve
Solve
The answers are 4.1712927296,-1.83795939622, 2.77485177345 and
-1.44151844011. These answers may or may not be solutions to the original
equation. You must verify each of the answers.
Check x=4.1712927296 by substituting 4.1712927296 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.
Check x=-1.83795939622 by substituting -1.83795939622 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.
Check x=2.77485177345 by substituting 2.77485177345 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.
Right Side:
Since the left side of the original equation is equal to the right side of
the original equation, the answer x=2.77485177345 is a solution to the
original equation.
Check x=-1.44151844011 by substituting -1.44151844011 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.
Right Side:
The solutions are 4.1712927296, -1.44151844011 , and 2.77485177345.
You can also check your answer by graphing the function
on your graphing calculator. The graph was formed by subtracting the right side of the original equation from the left side of the original equation. You will note that the three x-intercepts on the graph are located at x=4.1712927296, -1.44151844011 ,and 2.77485177345. This verifies the three solutions by a graphical method.
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Author:Nancy Marcus