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1/4p+3/4(p−8)=11+1/4(12p+4)

Sagot :

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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