Question

1/2+2/3(p-6)=3/4(p-8)​

Answer 1

$\sf{\red{\boxed{\bold{Solution}}}}$

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$\sf:\implies \: {\bold{ \dfrac{1}{2} + \dfrac{2}{3} ( p - 6 ) = \dfrac{3}{4} ( p - 8 )}}$

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$\sf:\implies \: {\bold{ \dfrac{1}{2} + \dfrac{2p - 12 }{3} = \dfrac{3p - 24}{4} }}$

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$\sf:\implies \: {\bold{ \dfrac{3 + 2 ( 2p - 12 ) }{6} = \dfrac{3p - 24}{4} }}$

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$\sf:\implies \: {\bold{ \dfrac{3 + 4p - 24 ) }{6} = \dfrac{3p - 24}{4} }}$

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$\sf:\implies \: {\bold{ \dfrac{ 4p - 21 }{6} = \dfrac{3p - 24}{4} }}$

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$\sf:\implies \: {\bold{ 4 ( 4p - 21 ) = 6( 3p - 24 ) }}$

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$\sf:\implies \: {\bold{ 16p - 84 = 18p - 144 }}$

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$\sf:\implies \: {\bold{ 18p - 16p = -84 + 144 }}$

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$\sf:\implies \: {\bold{ 2p = 60 }}$

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$\sf:\implies \: {\bold{ p = \dfrac{60}{2}}}$

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$\sf:\implies \: {\bold{ p = 30 }}$

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Answer 2

$\underline{\boxed{\sf{answer }}} \\ \\ \\ \implies \: \frac{1}{2} + \frac{2}{3} (p - 6) = \frac{3}{4} (p - 8) \\ \\ \implies \frac{1}{2} + \frac{2p - 12}{3} = \frac{3p - 24}{4} \\ \\ \implies \frac{3 + 2(2p - 12)}{6} = \frac{3p - 24}{4} \\ \\ \implies \frac{3 + 4p - 24}{6} = \frac{3p - 24}{4} \\ \\ \implies 4(4p - 21) = 6(3p - 24) \\ \\ \implies16p - 84 = 18p - 144 \\ \\ \implies18p - 16p = 144 - 84 \\ \\ \implies2p = 60 \\ \\ \implies \: p = \frac{ \cancel{60}}{ \cancel{2}} \\ \\ \implies \: \underline {\underline{p = 30}} \\ \\\\\underline{\boxed{\sf{p = 30 }}}$