Question

Find the value of p in equation: [ (7p/5) = (p-4) ]

Answer 1

Answer:

$\boxed{\sf p = -10}$

Step-by-step explanation:

$\sf Solve \: for \: p: \\ \sf \implies \frac{7p}{5} = p - 4 \\ \\ \sf Multiply \: both \: sides \: by \: 5: \\ \sf \implies \frac{5 \times 7p}{5} = 5(p - 4) \\ \\ \sf \frac{5 \times 7p}{5} = \cancel{ \frac{5}{5} } \times 7p = 7p : \\ \sf \implies 7p = 5(p - 4) \\ \\ \sf Expand \: out \: terms \: of \: the \: right \: hand \: side: \\ \sf \implies 7p = 5p - 20 \\ \\ \sf Subtract \: 5 p \: from \: both \: sides: \\ \sf \implies 7p - \boxed{ \sf 5p} = (5p - \boxed{ \sf 5p}) - 20 \\ \\ \sf 5p - 5p = 0 : \\ \sf \implies 7p - 5p = - 20 \\ \\ \sf 7p - 5p = 2p : \\ \sf \implies \boxed{ \sf 2p} = - 20 \\ \\ \sf Divide \: both \: sides \: of \: 2 p = - 20 \: by \: 2: \\ \sf \implies \frac{2p}{2} = \frac{ - 20}{2} \\ \\ \sf \frac{2p}{2} = \cancel{ \frac{2}{2} } \times p = p : \\ \sf \implies p = \frac{ - 20}{2} \\ \\ \sf \implies p = - \frac{ \cancel{2} \times 10}{ \cancel{2}} \\ \\ \sf \implies p = - 10$