Question

How do you solve `31=-(1+6p)+4(p+6)` using the distributive property?

Answer 1

`p=-4`

Explanation:

`31=color(red)(-1)(1+6p)color(red)(+4)(p+6)`

`"multiplying out the brackets (distributive property ) gives"`

`31=-1-6p+4p+24`

`31=23-2plarr" simplifying right side"`

`"subtract 23 from both sides"`

`31-23=cancel(23)cancel(-23)-2p`

`rArr-2p=8larr" reversing the equation"`

`"divide both sides by - 2"`

`(cancel(-2)color(white)(x)p)/cancel(-2)=8/(-2)`

`rArrp=-4`

`color(blue)"As a check"`

Substitute this value into the right side of the equation and if equal to the left side then it is the solution.

`-(1-24)+4(-4+6)=23+8=31="left side"`

`rArrp=-4" is the solution"`