Question

How do you solve `4( p - 3) = 3( p + 5)`?

Answer 1

`p=27`

Refer to the explanation for the process.

Explanation:

Solve:

`4(p-3)=3(p+5)`

Expand using the distributive property: `a(b+c)=ac+bc`.

`4p-12=3p+15`

Add `12` to both sides.

`4p=3p+15+12`

Simplify.

`4p=3p+27`

Subtract `3p` from both sides.

`4p-3p=27`

Simplify.

`p=27`

Answer 2

`p=27`

Explanation:

`"distribute brackets on both sides of the equation"`

`rArr4p-12=3p+15`

`"collect terms in p to one side and numeric values on"`
`"the other side"`

`"subtract 3p from both sides"`

`4p-3p-12=cancel(3p)cancel(-3p)+15`

`rArrp-12=15`

`"add 12 to both sides"`

`pcancel(-12)cancel(+12)=15+12`

`rArrp=27`

`color(blue)"As a check"`

Substitute this value into the equation and if both sides are equal then it is the solution.

`"left side "=(4xx24)=96`

`"right side "=(3xx32)=96`

`rArrp=27" is the solution"`

Answer 3

`p=27`

Explanation:

First multiply out the brackets:

`4p-12 = 3p+15`

Rearrange equation to have `p` on one side and numbers on the other:

`4p-3p=15+12`

Now solve the equation:

`p=27`