If $2 Q + 4 P = \frac{3 P - Q}{2 R}$ , express P in terms of Q and R. Find the value of P, when $R = - 2$ and $Q = 1$ .

P = \frac{(1 + 4 R)}{Q (1 - 2 R)}; - \frac{3}{14}

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P = \frac{Q (1 - 4 R)}{(1 - 2 R)}; - \frac{2}{17}

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P = \frac{Q (1 + 4 R)}{(3 - 8 R)}; - \frac{7}{19}

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p = \frac{Q (1 + 4 R)}{3 (1 - 2 R)}; - \frac{9}{19}

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Solution

The correct option is C $P = \frac{Q (1 + 4 R)}{(3 - 8 R)}; - \frac{7}{19}$
Given:
$2 Q + 4 P = \frac{3 P - Q}{2 R}$

Multiplying both sides by $2 R$ , we get

$(2 Q + 4 P) \times 2 R = 3 P - Q$

$4 Q R + 8 P R = 3 P - Q$

Subtracting $3 P$ from both sides, we get

$4 Q R + 8 P R - 3 P = - Q$

$8 P R - 3 P = - Q - 4 Q R$

Taking $P and Q common on LHS and RHS respectively$

$P (8 R - 3) = - Q (1 + 4 R)$

$P = \frac{Q (1 + 4 R)}{3 - 8 R}$

Putting $R = - 2 and Q = 1$ , we get

$P = \frac{1 (1 - 8)}{3 + 16} = \frac{- 7}{19}$

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