Let's solve the given equation step by step to find the value of [tex]\(d\)[/tex]:
Given equation:
[tex]\[
\frac{3}{2}(7 + 3d) = 3 + 3d
\][/tex]
### Step 1: Eliminate the fraction
To get rid of the fraction, multiply both sides of the equation by 2:
[tex]\[
2 \cdot \frac{3}{2}(7 + 3d) = 2 \cdot (3 + 3d)
\][/tex]
This simplifies to:
[tex]\[
3(7 + 3d) = 6 + 6d
\][/tex]
### Step 2: Distribute the multiplication on the left side
Distribute the 3 across the terms inside the parentheses:
[tex]\[
3 \cdot 7 + 3 \cdot 3d = 21 + 9d
\][/tex]
So the equation now is:
[tex]\[
21 + 9d = 6 + 6d
\][/tex]
### Step 3: Move all terms involving [tex]\(d\)[/tex] to one side and constants to the other side
Subtract [tex]\(6d\)[/tex] from both sides to get all terms involving [tex]\(d\)[/tex] on one side:
[tex]\[
21 + 9d - 6d = 6 + 6d - 6d
\][/tex]
This simplifies to:
[tex]\[
21 + 3d = 6
\][/tex]
Subtract 21 from both sides to get all constant terms on the other side:
[tex]\[
21 - 21 + 3d = 6 - 21
\][/tex]
This simplifies to:
[tex]\[
3d = -15
\][/tex]
### Step 4: Solve for [tex]\(d\)[/tex]
Divide both sides by 3:
[tex]\[
d = \frac{-15}{3}
\][/tex]
This simplifies to:
[tex]\[
d = -5
\][/tex]
Therefore, the value of [tex]\(d\)[/tex] is:
[tex]\[
\boxed{-5}
\][/tex]
