Question

solve the equation
$\frac{8p - 5}{7p + 1} = \frac{ - 2}{ \: \: \: \: 4}$
​

Answer 1

Explanation:

$\mathsf{\frac{8p-5}{7p+1}=\frac{-2}{4}==>\frac{8p-5}{7p+1}=\frac{-1}{2}}$

$\mathsf{==>2(8p-5)=-1(7p+1)}$

$\mathsf{==>16p-10=-7p-1}$

$\mathsf{==>16p+7p=-1+10}$

$\mathsf{==>23p=9}$

∴ $\mathsf{p=\frac{9}{23}}$

Verification:

LHS:

$\mathsf{\frac{8p-5}{7p+1}=\frac{8\times \frac{9}{23}-5}{7 \times \frac{9}{23}+1}}$

$\mathsf{=\frac{\frac{72-115}{23}}{\frac{63+23}{23}}=\frac{\frac{-43}{23}}{\frac{86}{23}}}$

$\mathsf{=\frac{-43}{86}=\frac{-1}{2}}$

RHS:

$\mathsf{\frac{-2}{4}=\frac{-1}{2}}$

LHS = RHS, hence verified.

Answer: p = 9/23

I hope this helps. :D

Answer 2

Answer:

p=9/23

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