Question

1/4p+3/4(p−8)=11+1/4(12p+4)

Answer 1

Answer:

$\boxed{\bold{p=-9}}$

Step-by-step explanation:

$\bold{ \cfrac{1}{4}\:p+\cfrac{3}{4}\left(p-8\right)=11+\cfrac{1}{4}\left(12p+4\right)}$

$\bold{\cfrac{1}{4}\left(12p+4\right)}$

Multiply fractions:

$\bold{\cfrac{1\times \left(12p+4\right)}{4}}$

$\bold{\cfrac{12p+4}{4}}$

$\bold{\cfrac{1}{4}\:p+\cfrac{3}{4}\left(p-8\right)=11+\cfrac{12p+4}{4}}$

Now, Multiply both sides by 4:

$\bold {\cfrac{1}{4}\:p\times \:4+\cfrac{3}{4}\left(p-8\right)\times \:4=11\times \:4+\cfrac{12p+4}{4}\times \:4}$

$\bold {p+3\left(p-8\right)=12p+48}$

Expand: Apply Distributive property:

$\bold{p+3p-24=12p+48}$

Combine like terms:

$\bold{(p+3p):4p}$

$\bold{4p-24=12p+48}$

Add 24 from both sides:

$\bold{4p-24+24=12p+48+24}$

$\bold{4p=12p+72}$

Subtract 12p from both sides:

$\bold{4p-12p=12p+72-12p}$

$\bold{-8p=72}$

Divide both sides by -8:

$\bold{\cfrac{-8p}{-8}=\cfrac{72}{-8}}$

$\bold{p=-9}$

______________________________________