Question

the latest online craze is a new game, khan on seven. you get 100 points for playing the game. in addition, you get 50 points for each seven - letter word you make with the ten letters you receive. sal wants to break the record, and he needs 18,000 or more points to do so. write an inequality to determine the number of seven - letter words, w, sal could make to break the record. 100 + 50w ≥ 18000 graph the solution set to this inequality. switch direction make circle open show calculator

Explanation:

Step1: Solve the inequality

$$\begin{align*} 100 + 50w&\geq18000\\ 50w&\geq18000 - 100\\ 50w&\geq17900\\ w&\geq\frac{17900}{50}\\ w&\geq358 \end{align*}$$

Step2: Graph the solution

Since \(w\geq358\), on the number - line, we make a closed circle at \(358\) (because the inequality is non - strict, i.e., includes equality) and shade to the right.

Answer:

The solution of the inequality \(100 + 50w\geq18000\) is \(w\geq358\). On the number - line, we have a closed circle at \(358\) and the line is shaded to the right of \(358\).