To solve the equation [tex]\( 6(d + 1) - 2d = 54 \)[/tex], follow these steps:
1. Distribute the 6 on the left side of the equation:
[tex]\[
6(d + 1) - 2d = 54
\][/tex]
becomes
[tex]\[
6d + 6 - 2d = 54
\][/tex]
2. Combine like terms:
[tex]\[
6d - 2d + 6 = 54
\][/tex]
simplifies to
[tex]\[
4d + 6 = 54
\][/tex]
3. Isolate the term with [tex]\( d \)[/tex] by subtracting 6 from both sides:
[tex]\[
4d + 6 - 6 = 54 - 6
\][/tex]
simplifies to
[tex]\[
4d = 48
\][/tex]
4. Solve for [tex]\( d \)[/tex] by dividing both sides by 4:
[tex]\[
d = \frac{48}{4}
\][/tex]
which simplifies to
[tex]\[
d = 12
\][/tex]
So, the solution is:
[tex]\[
\boxed{12}
\][/tex]
