Answer :
Let's solve the problem step-by-step to make [tex]\( d \)[/tex] the subject of the formula:
We have the equation:
[tex]\[ d - 7 = \frac{4d + 3}{e} \][/tex]
Step 1: Multiply both sides by [tex]\( e \)[/tex] to eliminate the fraction:
[tex]\[ e(d - 7) = 4d + 3 \][/tex]
Step 2: Distribute [tex]\( e \)[/tex] on the left side:
[tex]\[ ed - 7e = 4d + 3 \][/tex]
Step 3: Rearrange the equation to get all terms with [tex]\( d \)[/tex] on one side:
[tex]\[ ed - 4d = 3 + 7e \][/tex]
Step 4: Factor out [tex]\( d \)[/tex] from the left side:
[tex]\[ d(e - 4) = 3 + 7e \][/tex]
Step 5: Finally, solve for [tex]\( d \)[/tex] by dividing both sides by [tex]\( (e - 4) \)[/tex]:
[tex]\[ d = \frac{3 + 7e}{e - 4} \][/tex]
And that is the final expression for [tex]\( d \)[/tex] in terms of [tex]\( e \)[/tex].
We have the equation:
[tex]\[ d - 7 = \frac{4d + 3}{e} \][/tex]
Step 1: Multiply both sides by [tex]\( e \)[/tex] to eliminate the fraction:
[tex]\[ e(d - 7) = 4d + 3 \][/tex]
Step 2: Distribute [tex]\( e \)[/tex] on the left side:
[tex]\[ ed - 7e = 4d + 3 \][/tex]
Step 3: Rearrange the equation to get all terms with [tex]\( d \)[/tex] on one side:
[tex]\[ ed - 4d = 3 + 7e \][/tex]
Step 4: Factor out [tex]\( d \)[/tex] from the left side:
[tex]\[ d(e - 4) = 3 + 7e \][/tex]
Step 5: Finally, solve for [tex]\( d \)[/tex] by dividing both sides by [tex]\( (e - 4) \)[/tex]:
[tex]\[ d = \frac{3 + 7e}{e - 4} \][/tex]
And that is the final expression for [tex]\( d \)[/tex] in terms of [tex]\( e \)[/tex].
