Sure, let's solve the equation \( v = 5u - 3z \) for \( z \) step-by-step.
1. Given Equation:
[tex]\[
v = 5u - 3z
\][/tex]
2. Isolate the term involving \( z \):
To isolate the term involving \( z \), we need to get \( z \) by itself on one side of the equation. Let's move the term involving \( z \) to the other side by subtracting \( 5u \) from both sides.
[tex]\[
v - 5u = -3z
\][/tex]
3. Solve for \( z \):
To solve for \( z \), we need to isolate \( z \). This can be done by dividing both sides of the equation by \(-3\).
[tex]\[
z = \frac{v - 5u}{-3}
\][/tex]
4. Simplify the expression:
To simplify the fraction \(\frac{v - 5u}{-3}\), we can split the fraction into two parts:
[tex]\[
z = \frac{v}{-3} + \frac{5u}{-3}
\][/tex]
5. Simplify the signs:
The fractions can be written with positive denominators, which gives us:
[tex]\[
z = -\frac{v}{3} + \frac{5u}{3}
\][/tex]
6. Combine the fractions:
Combining the fractions, we get:
[tex]\[
z = \frac{5u - v}{3}
\][/tex]
Hence, solving for \( z \) in terms of \( v \) and \( u \), we get:
[tex]\[
z = \frac{5u}{3} - \frac{v}{3}
\][/tex]
