Note:
Problem 3.4c:
Answer:
Either or
Solve
Solve
The answers are 2,-1, 1.31774468788 and -1.51774468788. These
answers may or may not be solutions to the original equation. You must
verify each of the answers.
Check the solutions:
Check the answer 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.
Right Side:
Since the left side of the original equation is equal to the right side of
the original equation, the answer x=2 is a solution to the original
equation.
Check x=-1 by substituting -1 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 not equal to the right side
of the original equation, the answer x=-1 is not a solution to the
original equation. You could also note that the absolute value cannot be
negative, therefore no negative answer is valid.
Check x=1.31774468788 by substituting 1.31774468788 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=1.31774468788 is a solution to the
original equation.
Check x=-1.51774468788 by substituting -1.51774468788 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.
The solutions are 2 and 1.31774468788.
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 two x-intercepts on the graph are located at x=2 and 1.31774468788. This verifies the two solutions by a graphical method.
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Author:Nancy Marcus