###### Example2.2.14

Ann has budgeted a maximum of $$\300$$ for an appliance repair. The total cost of the repair can be modeled by $$89+110(h-0.25)\text{,}$$ where $$\89$$ is the initial cost and $$\110$$ is the hourly labor charge after the first quarter hour. Is $$2$$ a solution for $$h$$ in the inequality $$89+110(h-0.25)\le 300\text{?}$$

To determine if $$h=2$$ satisfies the inequality $$89+110(h-0.25)\le 300\text{,}$$ we will replace $$h$$ with $$2$$ and check if the statement is true or false:

\begin{align*} 89+110(h-0.25)\amp\le 300\\ 89+110(\substitute{2}-0.25)\amp\stackrel{?}{\le} 300\\ 89+110(1.75)\amp\stackrel{?}{\le} 300\\ 89+192.5\amp\stackrel{?}{\le} 300\\ 281.5\amp\stackrel{\checkmark}{\le} 300 \end{align*}

Thus $$2$$ is a solution for $$h$$ in the inequality $$89+110(h-0.25)\le 300\text{.}$$ In context, this means that Ann would stay within her $$\300$$ budget if $$2$$ hours of labor were performed.

in-context