Answer:
[tex]\boxed{\bold{p=-9}}[/tex]
Step-by-step explanation:
[tex]\bold{ \cfrac{1}{4}\:p+\cfrac{3}{4}\left(p-8\right)=11+\cfrac{1}{4}\left(12p+4\right)}[/tex]
[tex]\bold{\cfrac{1}{4}\left(12p+4\right)}[/tex]
Multiply fractions:
[tex]\bold{\cfrac{1\times \left(12p+4\right)}{4}}[/tex]
[tex]\bold{\cfrac{12p+4}{4}}[/tex]
[tex]\bold{\cfrac{1}{4}\:p+\cfrac{3}{4}\left(p-8\right)=11+\cfrac{12p+4}{4}}[/tex]
Now, Multiply both sides by 4:
[tex]\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}[/tex]
[tex]\bold {p+3\left(p-8\right)=12p+48}[/tex]
Expand: Apply Distributive property:
[tex]\bold{p+3p-24=12p+48}[/tex]
Combine like terms:
[tex]\bold{(p+3p):4p}[/tex]
[tex]\bold{4p-24=12p+48}[/tex]
Add 24 from both sides:
[tex]\bold{4p-24+24=12p+48+24}[/tex]
[tex]\bold{4p=12p+72}[/tex]
Subtract 12p from both sides:
[tex]\bold{4p-12p=12p+72-12p}[/tex]
[tex]\bold{-8p=72}[/tex]
Divide both sides by -8:
[tex]\bold{\cfrac{-8p}{-8}=\cfrac{72}{-8}}[/tex]
[tex]\bold{p=-9}[/tex]
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