Solve and checking 6p+1/3 + 1= 7p-3/2 – InterviewSolution

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Solve and checking 6p+1/3 + 1= 7p-3/2

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Solution:

Simplifying the EXPRESSION on L.H.S. of the equation by taking L.C.N., we get

$\longrightarrow \sf {\dfrac{6 \: p + 1 + <klux>3</klux>}{3} = \dfrac{7 \: p - 3}{2}} \\\\$

$\longrightarrow \sf {\dfrac{6 \: p + <klux>4</klux>}{3} = \dfrac{7 \: p - 3}{2}} \\\\$

By cross multiplying, we get

=> 2(6P + 4) = 3(7p - 3)

=> 12p + 8 = 21P - 9

=> 8 + 9 = 21p - 12p

=> 17 = 9p

=> 17/9 = p

Check:

$\sf {For \:p = \dfrac{17}{9}, L.H.S. \:reduces \: to \: \dfrac{ 6\bigg(\dfrac{17}{9 } \bigg) + 1}{3} + 1} \\\\$

$\longrightarrow \sf{ \dfrac{ \dfrac{34}{3} + 1 }{3} + 1 } \\\\$

$\longrightarrow \sf {\dfrac{37}{9} + 1} \\\\$

$\longrightarrow \sf { \dfrac{37 + 9}{9} } \\\\$

$\longrightarrow\sf{ \dfrac{46}{9}} \\\\$

$\longrightarrow \sf{R.H.S. = \dfrac{7 \dfrac{17}{9} - 3 }{2} } \\\\$

$\longrightarrow \sf {\dfrac{ \dfrac{119}{9} - 3 }{2}} \\ \\$

$\longrightarrow \sf { \dfrac{119 - 27}{9 \times 2}} \\\\$

$\longrightarrow \sf { \dfrac{92}{9 \times 2} } \\\\$

$\longrightarrow \sf { \dfrac{46}{9}}$

So L.H.S. = R.H.S.

Therefore,

p = 17/9 is a solution of the given equation.

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