QuestionSolve . What are the possible values of ?
Studdy Solution
STEP 1
Assumptions1. The equation is
. The absolute value function is defined as if and if
3. The solutions for can be real numbers
STEP 2
First, we need to isolate the absolute value on one side of the equation. We can do this by adding5 to both sides of the equation.
STEP 3
implify the right side of the equation.
STEP 4
Next, we need to remove the fraction on the left side. We can do this by multiplying both sides of the equation by3.
STEP 5
implify the right side of the equation.
STEP 6
Now, we need to solve for . The absolute value equation has two solutions and . Therefore, we have two equations to solve
STEP 7
Subtract9 from both sides of the first equation to isolate .
STEP 8
implify the right side of the first equation.
STEP 9
Divide both sides of the first equation by3 to solve for .
STEP 10
implify the right side of the first equation.
STEP 11
Subtract9 from both sides of the second equation to isolate .
STEP 12
implify the right side of the second equation.
STEP 13
Divide both sides of the second equation by3 to solve for .
STEP 14
implify the right side of the second equation.
The solutions of the equation are and .
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