To solve for the variable [tex]\( k \)[/tex] in the equation
[tex]\[
u = \frac{-2a - 3}{ka}
\][/tex]
follow these steps:
1. Isolate the fraction involving [tex]\( k \)[/tex]:
Given the equation:
[tex]\[
u = \frac{-2a - 3}{ka}
\][/tex]
2. Multiply both sides by [tex]\( ka \)[/tex] to eliminate the fraction:
[tex]\[
u \cdot ka = -2a - 3
\][/tex]
3. Rearrange the equation to isolate [tex]\( k \)[/tex]:
[tex]\[
uka = -2a - 3
\][/tex]
4. Solve for [tex]\( k \)[/tex] by isolating it on one side of the equation. First, divide both sides by [tex]\( ua \)[/tex]:
[tex]\[
k = \frac{-2a - 3}{ua}
\][/tex]
Therefore, the solution for [tex]\( k \)[/tex] in terms of the variables [tex]\( u \)[/tex] and [tex]\( a \)[/tex] is:
[tex]\[
k = \frac{-2a - 3}{ua}
\][/tex]
This represents the value of [tex]\( k \)[/tex] that satisfies the original equation.
