To make [tex]\( p \)[/tex] the subject of the equation [tex]\( q = \frac{3p}{p} + \frac{s}{z} \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
q = \frac{3p}{p} + \frac{s}{z}
\][/tex]
2. Simplify the term [tex]\( \frac{3p}{p} \)[/tex]. Since [tex]\( \frac{3p}{p} \)[/tex] simplifies to 3:
[tex]\[
q = 3 + \frac{s}{z}
\][/tex]
3. Isolate the fraction involving [tex]\( s \)[/tex] by subtracting 3 from both sides of the equation:
[tex]\[
q - 3 = \frac{s}{z}
\][/tex]
4. To isolate [tex]\( s \)[/tex], multiply both sides of the equation by [tex]\( z \)[/tex]:
[tex]\[
z(q - 3) = s
\][/tex]
5. Finally, to solve for [tex]\( p \)[/tex], note that in manipulating the equation, we have already isolated [tex]\( s \)[/tex]. Consider the rearrangement:
[tex]\[
s = z(q - 3)
\][/tex]
So, looking back at the equation simplification step, no direct dependency of [tex]\( p \)[/tex] on the new terms explicitly exists because [tex]\( p \)[/tex] is neither dependent on [tex]\( s \)[/tex] nor reappears in the simplified terms after [tex]\( \frac{3p}{p} = 3 \)[/tex].
Instead, recognize that:
Therefore, [tex]\( p \)[/tex] resolves as:
[tex]\[
p = \frac{s}{z(q - 3)}
\][/tex]
6. Summing it all together, we have:
[tex]\[
p = \frac{s}{z(q - 3)}
\][/tex]
