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If $Q-\dfrac{1}{3}P=30$ , which of the following correctly gives $P$ in terms of $Q$ ?

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Evaluate expression when two complex numbers are given

Full solution

Q. If

Q-\dfrac{1}{3}P=30

, which of the following correctly gives

P

in terms of

Q

?

Isolate P term: We are given the equation $Q - \frac{1}{3}P = 30$ and we need to solve for $P$ in terms of $Q$ . $\newline$ First, we will isolate the term containing $P$ on one side of the equation. $\newline$ Add $\frac{1}{3}P$ to both sides of the equation to move the term with $P$ to the right side. $\newline$ $Q - \frac{1}{3}P + \frac{1}{3}P = 30 + \frac{1}{3}P$
Simplify left side: Now, we simplify the left side of the equation by combining like terms. $\newline$ $Q + 0 = 30 + (\frac{1}{3})P$ $\newline$ This simplifies to: $\newline$ $Q = 30 + (\frac{1}{3})P$
Isolate P: Next, we need to isolate P. To do this, we subtract $30$ from both sides of the equation. $\newline$ $Q - 30 = (\frac{1}{3})P$
Multiply by $3$ : Finally, to solve for $P$ , we multiply both sides of the equation by $3$ to get rid of the fraction. $\newline$ $3(Q - 30) = P$
Distribute $3$ : Now, we distribute the $3$ on the left side of the equation. $3Q - 90 = P$
Express $P$ in terms of $Q$ : We have now expressed $P$ in terms of $Q$ . $P = 3Q - 90$

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