Question

What is the answer of solve the following equations and verify your answer ​ ​

Answer 1

Answer:

Solution !!

$\implies{\sf{ \dfrac{p + 7}{p - 6} = \dfrac{1}{3}}}$

By cross multiplication :

$\implies{\sf{ {3(p + 7)} = 1{(p - 6)} }}$

$\implies{\sf{3p + 27 = p - 6 }}$

$\implies{\sf{3p - p = - 6 - 21}}$

$\implies{\sf{2p = - 27}}$

$\implies{\sf{\underline{\underline{\red{p = \dfrac{ - 27}{2}}}}}}$

Hence, the value of p is -27/2

$\begin{gathered}\end{gathered}$

Verification !!

$\implies{\sf{ \dfrac{p + 7}{p - 6} = \dfrac{1}{3}}}$

Substituting the value of (p = -27/2)

$\implies{\sf{ \dfrac{ \dfrac{ - 27}{2} + 7}{ \dfrac{ - 27}{2} - 6} = \dfrac{1}{3}}}$

$\implies{\sf{ \dfrac{ \dfrac{ - 27 + 14}{2}}{ \dfrac{ - 27 - 12}{2} } = \dfrac{1}{3}}}$

$\implies{\sf{ \dfrac{ \dfrac{ - 13}{2}}{ \dfrac{ - 39}{2} } = \dfrac{1}{3}}}$

$\implies{\sf{ \dfrac{ - 13}{2} \times \dfrac{2}{ - 39} = \dfrac{1}{3}}}$

$\implies{\sf{ \dfrac{ - 13}{\cancel{2}} \times \dfrac{\cancel{2}}{ - 39} = \dfrac{1}{3}}}$

$\implies{\sf{ \dfrac{ - 13}{ - 39} = \dfrac{1}{3}}}$

$\implies{\sf{ \cancel{\dfrac{ - 13}{ - 39}} = \dfrac{1}{3}}}$

$\implies{\sf{ \dfrac{1}{3} = \dfrac{1}{3}}}$

$\implies{\sf{\underline{\underline{\red{LHS = RHS}}}}}$

Hence Verified!

$\underline{\rule{220pt}{3pt}}$

Answer 2

Explanation :

By doing cross multiplication, we get-----

=>p-6=3(p+7)

=>p-6=3p+21 =>p-3p=21+6

=>-2p=27

=>p=27/-2

=>p=-27/2

Verification:

By,putting the value of p in the equation, we get----

(LHS)=(-27/2+7)/(-27/2-6)=1/3(RHS)

=>(-27+14/2)/(-27-12/2)=1/3

=>(-13/2)/(-39/2)=1/3

=>-13/2×2/-39=1/3

=>1/3=1/3

Hence,LHS=RHS verified.