Let's solve the given equation step-by-step to isolate and solve for [tex]\( y \)[/tex].
Given equation:
[tex]\[ 12y + d = -19y + t \][/tex]
Step 1: Move all terms involving [tex]\( y \)[/tex] to one side of the equation.
We can start by adding [tex]\( 19y \)[/tex] to both sides of the equation:
[tex]\[ 12y + 19y + d = -19y + 19y + t \][/tex]
[tex]\[ 31y + d = t \][/tex]
Step 2: Move the constant term to the other side of the equation.
Next, subtract [tex]\( d \)[/tex] from both sides of the equation:
[tex]\[ 31y + d - d = t - d \][/tex]
[tex]\[ 31y = t - d \][/tex]
Step 3: Solve for [tex]\( y \)[/tex] by dividing both sides by 31.
To isolate [tex]\( y \)[/tex], divide both sides of the equation by 31:
[tex]\[ y = \frac{t - d}{31} \][/tex]
Therefore, the correct form of the equation rewritten to solve for [tex]\( y \)[/tex] is:
[tex]\[ y = \frac{t - d}{31} \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{D\ y = \frac{t - d}{31}} \][/tex]
