Question

1. a physicist records the molecular weight of a few compounds. the physicist uses the inequality (50leq0.25x + 4.5leq150) to determine the weight of compounds that weight between 50 grams per mole and 150 grams per mole. solve the inequality.
2. a student is ordering a flower arrangement. she can choose any combination of roses and carnations for her flower arrangement, and she does not want to spend more than $30. roses cost $3 each and carnations cost $2 each. write an inequality that represents all possible combinations of x roses and y carnations.
3. graph the solution to the inequality (yleq\frac{2}{3}x - 4).

Explanation:

Step1: Subtract 4.5 from all parts

$$\begin{align*} 50 - 4.5&\leq0.25x+4.5 - 4.5\leq150 - 4.5\\ 45.5&\leq0.25x\leq145.5 \end{align*}$$

Step2: Divide all parts by 0.25

$$\begin{align*} \frac{45.5}{0.25}&\leq\frac{0.25x}{0.25}\leq\frac{145.5}{0.25}\\ 182&\leq x\leq582 \end{align*}$$

Answer:

$182\leq x\leq582$