Let's solve the given equation step by step:
1. The original equation is:
[tex]\[
-\frac{5}{6}e - \frac{2}{3}e = -24
\][/tex]
2. Combine the like terms on the left-hand side (LHS). To do this, let's get a common denominator for the fractions. The common denominator of 6 and 3 is 6.
[tex]\[
-\frac{5}{6}e - \frac{4}{6}e = -24
\][/tex]
3. Now, combine the fractions:
[tex]\[
-\left(\frac{5}{6}e + \frac{4}{6}e\right) = -24
\][/tex]
[tex]\[
-\frac{9}{6}e = -24
\][/tex]
4. Simplify the fraction on the LHS:
[tex]\[
-\frac{3}{2}e = -24
\][/tex]
5. To isolate [tex]\( e \)[/tex], multiply both sides of the equation by the reciprocal of [tex]\(-\frac{3}{2}\)[/tex], which is [tex]\(-\frac{2}{3}\)[/tex]:
[tex]\[
e = -24 \times \left(-\frac{2}{3}\right)
\][/tex]
6. Perform the multiplication:
[tex]\[
e = 16
\][/tex]
Therefore, the solution to the equation is:
[tex]\[
e = 16
\][/tex]
