Answer :
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].
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].