Question

1/4p+3/4(p−8)=11+1/4(12p+4)

Answer 1

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

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* \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* \:4+\cfrac{3}{4}\left(p-8\right)* \:4=11* \:4+\cfrac{12p+4}{4}* \: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}`

______________________________________