Given the equation [tex]P = s_1 t - s_2 t[/tex], which equation is solved for [tex]t[/tex]?

A. [tex]t = P \left( s_1 - s_2 \right)[/tex]
B. [tex]t = P - s_1 + s_2[/tex]
C. [tex]t = \frac{P}{s_1 - s_2}[/tex]
D. [tex]t = \frac{P}{s_1 + s_2}[/tex]



Answer :

Certainly! Let's analyze the given problem step by step:

We start with the equation:

[tex]\[ P = s_1 t - s_2 t \][/tex]

Notice that both terms on the right-hand side contain the variable [tex]\( t \)[/tex]. We can factor [tex]\( t \)[/tex] out of the right-hand side:

[tex]\[ P = t (s_1 - s_2) \][/tex]

Our goal is to solve for [tex]\( t \)[/tex]. To isolate [tex]\( t \)[/tex], we can divide both sides of the equation by the factor [tex]\( (s_1 - s_2) \)[/tex]:

[tex]\[ t = \frac{P}{s_1 - s_2} \][/tex]

Therefore, the equation solved for [tex]\( t \)[/tex] is:

[tex]\[ t = \frac{P}{s_1 - s_2} \][/tex]

Among the given options, the correct one is:

[tex]\[ \bigoplus_{t=} \frac{P}{s_1 - s_2} \][/tex]

This is the simplified and accurate solution.