Let's solve the equation [tex]\( 12y + d = -19y + t \)[/tex] step-by-step to find the correct expression for [tex]\( y \)[/tex].
1. Start with the given equation:
[tex]\[
12y + d = -19y + t
\][/tex]
2. Combine the [tex]\( y \)[/tex]-terms on one side of the equation. To do this, add [tex]\( 19y \)[/tex] to both sides:
[tex]\[
12y + 19y + d = t
\][/tex]
Simplify:
[tex]\[
31y + d = t
\][/tex]
3. Isolate [tex]\( y \)[/tex] by subtracting [tex]\( d \)[/tex] from both sides:
[tex]\[
31y = t - d
\][/tex]
4. Finally, solve for [tex]\( y \)[/tex] by dividing both sides by 31:
[tex]\[
y = \frac{t - d}{31}
\][/tex]
So, the equation [tex]\( 12y + d = -19y + t \)[/tex] correctly rewritten to solve for [tex]\( y \)[/tex] is:
[tex]\[
y = \frac{t - d}{31}
\][/tex]
From the options given:
- A. [tex]\( y = 31(t - d) \)[/tex] is incorrect.
- [tex]\( y = \frac{1 + d}{-7} \)[/tex] is incorrect.
- [tex]\( y = \frac{L - d}{31} \)[/tex] is incorrect (and introduces an undefined variable [tex]\( L \)[/tex]).
- [tex]\( y = -7(t + d) \)[/tex] is incorrect.
None of the options seem to match the correct solution [tex]\( y = \frac{t - d}{31} \)[/tex].
Therefore, if we assume the correct form for [tex]\( y \)[/tex] based on solving the equation is correct, the exact solution from the steps shown would be:
[tex]\[
y = \frac{t - d}{31}
\][/tex]
None of the given choice options A, B, C, or D is correct in this context.
