Unit 2B Review: Linear Inequalities and Systems

Vocabulary practice flashcards covering linear inequalities, systems of constraints, and real-world modeling problems from the Unit 2B Review worksheet.

Luncheon Attendance Constraint

The condition modeling that at least $16$ staff members are expected to attend the luncheon, expressed algebraically as $n \ge 16$, where $n$ represents the number of attendees.

Luncheon Sandwich Quantity Relationship

The equation representing the principal's plan to prepare two sandwiches for each attendee: $s = 2n$, where $s$ is the number of sandwiches and $n$ is the number of attendees.

Luncheon Budget Constraint

The inequality representing that the total cost of sandwiches at $\$3$ each must not exceed the principal's budget of $\$225$, written as $3s \le 225$.

Elena's Cooking Class Budget Inequality

The linear inequality representing the constraint that Elena spends strictly less than $\$50$ on $d$ pounds of dried chili peppers at $\$16.95$ per pound and $h$ pounds of corn husks at $\$6.49$ per pound: $16.95d + 6.49h < 50$.

Feasibility Check for $(2, 4)$ in Cooking Class Budget

The calculation determining whether Elena can buy $2$ pounds of dried chili peppers and $4$ pounds of corn husks: $16.95(2) + 6.49(4) = 33.90 + 25.96 = 59.86$, which is not less than $\$50$, making this purchase outside the budget.

Hair Stylist Daily Income Constraint

The inequality modeling the requirement that the stylist must make a minimum of $\$150$ in a day from haircuts charging $\$15$ each ($x$) and coloring charging $\$30$ each ($y$), represented as $15x + 30y \ge 150$.

Hair Stylist Daily Work Hours Constraint

The inequality modeling that the stylist works at most $8$ hours in a day, given that a haircut takes $30\,\text{minutes}$ ($0.5\,\text{hours}$) and coloring takes $2\,\text{hours}$, expressed as $0.5x + 2y \le 8$.

Elena's Jewelry Gift Budget Inequality

The inequality representing spending no more than $\$30$ on $b$ bracelets at $\$3$ each and $n$ necklaces at $\$5$ each, expressed as $3b + 5n \le 30$.

Texting Plan Cost Comparison Inequality

The inequality expressing that Plan A ($10\,\text{cents}$ per text) is cheaper than Plan B ($\$12$ monthly fee plus $2\,\text{cents}$ per text) for $x$ texts sent or received: $0.10x < 12 + 0.02x$.

System of Inequalities Boundary Lines (Source 5)

The two dashed boundary lines defined by $y = 3x + 2$ (shaded above for $y > 3x + 2$) and $-4x + 3y = 12$ or $y = \frac{4}{3}x + 4$ (shaded below for $-4x + 3y < 12$).

Solution to a System of Linear Inequalities

Any coordinate point $(x, y)$ that simultaneously satisfies all inequalities in the system, lying strictly within the overlapping intersection of their graphed solution regions.