QuestionSolve the equation . What are the solutions? A. List them or B. Is it empty?
Studdy Solution
STEP 1
Assumptions1. The absolute value of a number is the distance of the number from zero on the number line, regardless of the direction. Therefore, it is always non-negative. . If , where is a positive real number, then or .
STEP 2
The given equation isWe can split this into two equations according to the property mentioned in assumption2.
and
STEP 3
Let's solve the first equation for .
Subtract1 from both sides of the equation.
STEP 4
implify the right side of the equation.
STEP 5
To isolate , divide both sides of the equation by .
STEP 6
implify the right side of the equation.
STEP 7
Now, let's solve the second equation for .
Subtract1 from both sides of the equation.
STEP 8
implify the right side of the equation.
STEP 9
To isolate , divide both sides of the equation by .
STEP 10
implify the right side of the equation.
STEP 11
So, the solution set is .
The correct choice is A. The solution set is .
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