Unit #2 Study Guide - Linear Inequalities

Flashcards covering key problems, inequality modeling, boundary line rules, and algebraic operations from the Unit 2 Study Guide.

In Problem 2 of the study guide, Octavia wants to spend no more than a total of $55$ dollars on desserts. If each pie costs $4$ dollars, each cake costs $8$ dollars, $x$ represents the number of pies, and $y$ represents the number of cakes, what inequality models this situation?

$$4x + 8y \le 55$$

In Problem 5, Lucas is given the inequality $-15P + 10D < 50$. What type of boundary line is used when graphing this inequality?

A dashed (or dotted) boundary line is used because the inequality symbol is strictly less than ($<$).

In Problem 5, when solving the inequality $-15P + 10D < 50$ for $P$, what happens to the inequality symbol and what is the solved inequality?

Dividing both sides by $-15$ reverses the inequality symbol from $<$ to $>$, resulting in $P > \frac{50 - 10D}{-15}$ (which simplifies to $P > \frac{2}{3}D - \frac{10}{3}$).

In Problem 4, given the inequality $I \ge 150 + 0.15s$ representing income $I$ in dollars based on sales $s$, what are the steps to isolate sales $s$?

Subtract $150$ from both sides to get $I - 150 \ge 0.15s$, then divide both sides by $0.15$ to get $s \le \frac{I - 150}{0.15}$.

In Problem 1, Marcy has $12$ hours to work on making bracelets ($x$) and keychains ($y$), represented by the inequality $2x + 3y \le 12$. What does the coefficient $2$ represent in this context?

The coefficient $2$ represents the number of hours it takes Marcy to make one bracelet ($x$).