# 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?

Jun 23, 2018

$n = 8$

#### Explanation:

Set $h = 39 = 4 n + 7$

Subtract 7 from both sides

$\textcolor{g r e e n}{39 = 4 n + 7 \textcolor{w h i t e}{\text{dddd")->color(white)("dddd}} 39 \textcolor{red}{- 7} = 4 n + 7 \textcolor{red}{- 7}}$

$\textcolor{w h i t e}{\text{dddddddddddddd")->color(white)("ddddd")32color(white)("d")=4ncolor(white)("d}} + 0$

Divide both sides by 4

$\textcolor{g r e e n}{32 = 4 n \textcolor{w h i t e}{\text{ddddddd")->color(white)("dddd}} \frac{32}{\textcolor{red}{4}} = \frac{4}{\textcolor{red}{4}} n}$

But $\frac{4}{4}$ is the same as 1 and $1 \times n = n$ giving:

$\frac{32}{4} = n$

$\frac{32 \div 4}{4 \div 4} = \frac{8}{1} = n = 8$

Written as per convention

$n = 8$

Jun 23, 2018

$8 \text{ years}$

#### Explanation:

$\text{we have to solve the equation for n}$

$4 n + 7 = 39$

$\text{subtract 7 from both sides}$

$4 n = 39 - 7 = 32$

$\text{divide both sides by 4}$

$\frac{\cancel{4} n}{\cancel{4}} = \frac{32}{4} \Rightarrow n = 8$