Question

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

Answer 1

Solution:

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

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

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

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.