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]
