To solve the equation [tex]\(\frac{v k}{D + y} = 5\)[/tex] for [tex]\(y\)[/tex], follow these steps:
1. Rewrite the equation: Start by isolating the variable term on one side of the equation:
[tex]\[
\frac{v k}{D + y} = 5
\][/tex]
2. Clear the fraction: Multiply both sides of the equation by [tex]\(D + y\)[/tex] to eliminate the denominator:
[tex]\[
v k = 5(D + y)
\][/tex]
3. Distribute the right-hand side: Expand the right-hand side of the equation:
[tex]\[
v k = 5D + 5y
\][/tex]
4. Isolate the variable term: Subtract [tex]\(5D\)[/tex] from both sides to isolate the term containing [tex]\(y\)[/tex]:
[tex]\[
v k - 5D = 5y
\][/tex]
5. Solve for [tex]\(y\)[/tex]: Finally, divide both sides of the equation by 5:
[tex]\[
y = \frac{v k - 5D}{5}
\][/tex]
This solution can be simplified to:
[tex]\[
y = -D + \frac{k v}{5}
\][/tex]
So the solution for [tex]\(y\)[/tex] is:
\[
y = -D + \frac{k v}{5}
