Answer :

To solve for [tex]\( e \)[/tex] in the given equation [tex]\( 0.75(8 + e) = 2 - 1.25e \)[/tex]:

1. Distribute the [tex]\( 0.75 \)[/tex] on the left side:
[tex]\[ 0.75 \times 8 + 0.75 \times e = 6 + 0.75e \][/tex]
So the original equation becomes:
[tex]\[ 6 + 0.75e = 2 - 1.25e \][/tex]

2. Combine like terms by adding [tex]\( 1.25e \)[/tex] to both sides:
[tex]\[ 6 + 0.75e + 1.25e = 2 \][/tex]
Simplifying the left side, we get:
[tex]\[ 6 + 2e = 2 \][/tex]

3. Isolate the term with [tex]\( e \)[/tex] by subtracting 6 from both sides:
[tex]\[ 2e = 2 - 6 \][/tex]
Simplifying the right side, we have:
[tex]\[ 2e = -4 \][/tex]

4. Solve for [tex]\( e \)[/tex] by dividing both sides by 2:
[tex]\[ e = \frac{-4}{2} \][/tex]
[tex]\[ e = -2 \][/tex]

So, the exact solution is:
[tex]\[ e = -2 \][/tex]