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# Analyzing One-Variable Inequalities in Context

## Analyzing One-Variable Inequalities in Context 1.9 - Solution

a
We are told that the drama class wants to raise at least $\2500.$ In an inequality, we would represent this by saying that the target sum has to be greater than or equal to $\2500.$ $\begin{gathered} \text{Target sum}\geq 2500 \end{gathered}$ The target sum is the earnings from ticket sale and the donations of $\470.$ $\begin{gathered} \text{Earnings from ticket sale}+470\geq 2500 \end{gathered}$ If we let $x$ represent the number of tickets the drama class needs to sell, the product of $x$ and the price of a single ticket, $\10,$ represents the earnings from ticket sale. $\begin{gathered} 10x+470 \geq 2500 \end{gathered}$ By solving the inequality for $x,$ we can find the number of tickets they need to sell.
$10x+470 \geq 2500$
$10x\geq2030$
$x\geq203$
The drama class has to sell at least $203$ tickets to raise $\2500.$
b

This inequality tells us that all values greater than or equal to $203$ will satisfy the inequality. Notice that $x$ can equal $203,$ which we show with a closed circle on the number line.