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Part 1
Solve the equation.
2 StartAbsoluteValue 2 y minus 6 EndAbsoluteValue minus 3 equals 3
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Part 1
Select the correct choice​ and, if​ necessary, fill in the answer box in your choice below.
A.
yequals
  
enter your response here
​(Type an integer or a simplified fraction. Use a comma to separate answers as​ needed.)
B.
There is no solution.

1 answer

To solve the equation \(2 |2y - 6| - 3 = 3\), we first isolate the absolute value expression.

  1. Add 3 to both sides: \[ 2 |2y - 6| = 6 \]

  2. Divide both sides by 2: \[ |2y - 6| = 3 \]

Now we can solve for \(y\) by considering the definition of absolute value. This gives us two cases to solve:

Case 1: \[ 2y - 6 = 3 \] Add 6 to both sides: \[ 2y = 9 \] Divide by 2: \[ y = \frac{9}{2} \]

Case 2: \[ 2y - 6 = -3 \] Add 6 to both sides: \[ 2y = 3 \] Divide by 2: \[ y = \frac{3}{2} \]

So, the solutions to the equation \(2 |2y - 6| - 3 = 3\) are:

\[ y = \frac{9}{2}, \frac{3}{2} \]

Thus, the correct choice is: A. \[ y = \frac{9}{2}, \frac{3}{2} \]