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\(\newcommand{\abs}[1]{\left\lvert#1\right\rvert}\newcommand{\substitute}[1]{{\color{blue}{{#1}}}}\newcommand{\amp}{&}\)

While camping, the height (in feet) inside a tent when you are $d$ ft from the north side of the tent is given by the formula $h=-2\abs{d-3}+6\text{.}$

When you are $5$ ft from the north side, the height will be
.

When you are $2.5$ ft from the north side, the height will be
.

Solution

When $d=5\text{,}$ we have:
$\begin{aligned} h\amp= -2\abs{d-3}+6\\ \amp= -2\abs{\substitute{5}-3}+6\\ \amp= -2\abs{2}+6\\ \amp= -2(2)+6\\ \amp= -4+6\\ \amp=2 \end{aligned}$
Thus, when you are $5$ ft from the north side, the height in the tent is $2$ ft.

When $d=2.5\text{,}$ we have:
$\begin{aligned} h\amp= -2\abs{d-3}+6\\ \amp= -2\abs{\substitute{2.5}-3}+6\\ \amp= -2\abs{-0.5}+6\\ \amp= -2(0.5)+6\\ \amp=-1+6\\ \amp=5 \end{aligned}$
Thus, when you are $2.5$ ft from the north side, the height in the tent is $5$ ft.

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