Answer :
Sure! Let's go through the steps to make [tex]\( d \)[/tex] the subject of the formula:
We start with the given equation:
[tex]\[ d - 7 = \frac{4d + 3}{e} \][/tex]
Hannah's goal is to isolate [tex]\( d \)[/tex]. Here's how she can do it step by step:
1. Multiply both sides by [tex]\( e \)[/tex] to eliminate the fraction:
[tex]\[ e(d - 7) = 4d + 3 \][/tex]
At this point, [tex]\( \square = 4d + 3 \)[/tex], so we can fill in the first box with [tex]\( e(d - 7) \)[/tex].
2. Distribute [tex]\( e \)[/tex] on the left side:
[tex]\[ ed - 7e = 4d + 3 \][/tex]
3. Re-arrange the equation to move all terms involving [tex]\( d \)[/tex] to one side:
[tex]\[ ed - 4d = 3 + 7e \][/tex]
4. Factor [tex]\( d \)[/tex] from the left side:
[tex]\[ d(e - 4) = 3 + 7e \][/tex]
Here, the box that follows [tex]\( d( \square ) \)[/tex] is the factor of [tex]\( d \)[/tex], which is [tex]\( e - 4 \)[/tex].
5. Divide both sides by [tex]\( (e - 4) \)[/tex] to solve for [tex]\( d \)[/tex]:
[tex]\[ d = \frac{3 + 7e}{e - 4} \][/tex]
Finally, we have isolated [tex]\( d \)[/tex] and can thus complete the missing parts in the formatted solution:
- The first box is [tex]\( e(d - 7) \)[/tex]
- The second box, after rearranging the terms, is [tex]\( 3 + 7e \)[/tex]
- The equation for [tex]\( d \)[/tex] is [tex]\( \frac{3 + 7e}{e - 4} \)[/tex]
So, [tex]\( d = \frac{3 + 7e}{e - 4} \)[/tex] is the solution.
We start with the given equation:
[tex]\[ d - 7 = \frac{4d + 3}{e} \][/tex]
Hannah's goal is to isolate [tex]\( d \)[/tex]. Here's how she can do it step by step:
1. Multiply both sides by [tex]\( e \)[/tex] to eliminate the fraction:
[tex]\[ e(d - 7) = 4d + 3 \][/tex]
At this point, [tex]\( \square = 4d + 3 \)[/tex], so we can fill in the first box with [tex]\( e(d - 7) \)[/tex].
2. Distribute [tex]\( e \)[/tex] on the left side:
[tex]\[ ed - 7e = 4d + 3 \][/tex]
3. Re-arrange the equation to move all terms involving [tex]\( d \)[/tex] to one side:
[tex]\[ ed - 4d = 3 + 7e \][/tex]
4. Factor [tex]\( d \)[/tex] from the left side:
[tex]\[ d(e - 4) = 3 + 7e \][/tex]
Here, the box that follows [tex]\( d( \square ) \)[/tex] is the factor of [tex]\( d \)[/tex], which is [tex]\( e - 4 \)[/tex].
5. Divide both sides by [tex]\( (e - 4) \)[/tex] to solve for [tex]\( d \)[/tex]:
[tex]\[ d = \frac{3 + 7e}{e - 4} \][/tex]
Finally, we have isolated [tex]\( d \)[/tex] and can thus complete the missing parts in the formatted solution:
- The first box is [tex]\( e(d - 7) \)[/tex]
- The second box, after rearranging the terms, is [tex]\( 3 + 7e \)[/tex]
- The equation for [tex]\( d \)[/tex] is [tex]\( \frac{3 + 7e}{e - 4} \)[/tex]
So, [tex]\( d = \frac{3 + 7e}{e - 4} \)[/tex] is the solution.
