Question

The height `(h)` of a tree after `(n)` years is given by the equation `h=4n+7`. In how many years will the height be 39 feet?

Answer 1

`n=8`

Explanation:

Set `h=39=4n+7`

Subtract 7 from both sides

`color(green)(39=4n+7color(white)("dddd")->color(white)("dddd")39color(red)(-7) =4n+7color(red)(-7))`

`color(white)("dddddddddddddd")->color(white)("ddddd")32color(white)("d")=4ncolor(white)("d")+0`

Divide both sides by 4

`color(green)(32=4ncolor(white)("ddddddd")->color(white)("dddd")32/color(red)(4)=4/color(red)(4) n)`

But `4/4` is the same as 1 and `1xxn=n` giving:

`32/4=n`

`(32-:4)/(4-:4) = 8/1=n=8`

Written as per convention

`n=8`

Answer 2

`8" years"`

Explanation:

`"we have to solve the equation for n"`

`4n+7=39`

`"subtract 7 from both sides"`

`4n=39-7=32`

`"divide both sides by 4"`

`(cancel(4) n)/cancel(4)=32/4rArrn=8`