Hannah was asked to make [tex]d[/tex] the subject of the formula:

[tex]d - 7 = \frac{4d + 3}{e}[/tex]

Complete Hannah's steps to her final answer:

[tex]
\begin{aligned}
\text{Step 1: } & \quad e(d - 7) = 4d + 3 \\
\text{Step 2: } & \quad ed - 7e = 4d + 3 \\
\text{Step 3: } & \quad ed - 4d = 3 + 7e \\
\text{Step 4: } & \quad d(e - 4) = 3 + 7e \\
\text{Step 5: } & \quad d = \frac{3 + 7e}{e - 4}
\end{aligned}
[/tex]

Let's solve for [tex]\( d \)[/tex] in the formula [tex]\( d - 7 = \frac{4d + 3}{e} \)[/tex] by rearranging the equation step-by-step.

1. Clear the fraction: Multiply both sides of the equation by [tex]\( e \)[/tex] to eliminate the fraction.

[tex]\[
e(d - 7) = 4d + 3
\][/tex]

2. Distribute [tex]\( e \)[/tex]: Distribute [tex]\( e \)[/tex] on the left side of the equation.

[tex]\[
ed - 7e = 4d + 3
\][/tex]

3. Rearrange the terms: Get all terms involving [tex]\( d \)[/tex] on one side of the equation and constant terms on the other side.

[tex]\[
ed - 4d = 7e + 3
\][/tex]

4. Factor out [tex]\( d \)[/tex]: Factor [tex]\( d \)[/tex] from the left side of the equation.

[tex]\[
d(e - 4) = 7e + 3
\][/tex]

5. Solve for [tex]\( d \)[/tex]: Divide both sides by [tex]\( (e - 4) \)[/tex] to isolate [tex]\( d \)[/tex].

[tex]\[
d = \frac{7e + 3}{e - 4}
\][/tex]

So, [tex]\( d \)[/tex] is the subject of the formula and the final answer is [tex]\( d = \frac{7e + 3}{e - 4} \)[/tex].