To solve for [tex]\( S \)[/tex] in the equation
[tex]\[ V = \frac{E - 7}{K(U + S)} \][/tex]
we will start by isolating [tex]\( S \)[/tex]. Here is the step-by-step process:
1. Multiply both sides by [tex]\( K(U + S) \)[/tex] to eliminate the denominator:
[tex]\[ V \cdot K(U + S) = E - 7 \][/tex]
2. Distribute [tex]\( VK \)[/tex] on the left side:
[tex]\[ VKU + VKS = E - 7 \][/tex]
3. Isolate the term containing [tex]\( S \)[/tex] (subtract [tex]\( VKU \)[/tex] from both sides):
[tex]\[ VKS = E - 7 - VKU \][/tex]
4. Solve for [tex]\( S \)[/tex] by dividing both sides by [tex]\( VK \)[/tex]:
[tex]\[ S = \frac{E - 7 - VKU}{VK} \][/tex]
5. Simplify the right side:
[tex]\[ S = \frac{E - 7}{VK} - \frac{VKU}{VK} \][/tex]
6. Further simplify:
Since [tex]\(\frac{VKU}{VK} = U\)[/tex],
[tex]\[ S = \frac{E - 7}{VK} - U \][/tex]
7. Combine the terms into one fraction:
[tex]\[ S = \frac{E - 7 - VKU}{VK} \][/tex]
So, the solution for [tex]\( S \)[/tex] is:
[tex]\[ S = \frac{E - 7 - VKU}{VK} \][/tex]
Or equivalently:
[tex]\[ S = \frac{E - KUV - 7}{KV} \][/tex]
Therefore, the solutions for [tex]\( S \)[/tex] is:
[tex]\[ S = \frac{E - KUV - 7}{KV} \][/tex]
