Unit 1A Review Notes

Evaluated expressions using order of operations (PEMDAS):
- $\frac{20 + 3 \cdot 5}{7 + 3}$
- $\frac{25 - 3 \cdot (5)^2}{-(7 - 3^2)}$
Solved linear equations:
- $105 + 45x = 30x + 15$
- $-\frac{x}{5} + 8 = -x + 20$
Rearranged literal equations for specified variables:
- Solve $A = \pi r^2$ for $\pi$ : $\pi = \frac{A}{r^2}$
- Solve $12x + 2y = -10$ for $y$ : $y = -6x - 5$
- Solve sphere volume $V = \frac{4}{3}\pi r^3$ for $r^3$ : $r^3 = \frac{3V}{4\pi}$
- Evaluated $r^3$ and $r$ given $V = 33.49$ and $\pi = 3.14$ : $r^3 = 8$ and $r = 2$
Simplified unfinished expressions and matched equivalent solution sets:
- $10(x - 3) + 20 = 10x - 10$ , which is equivalent to $2(5x - 5)$

Solved single-variable inequality:
- $-4(x + 3) < 64 \rightarrow x > -19$
Solved compound inequalities:
- $-5 < 4x - 5 < 19 \rightarrow 0 < x < 6$
- $-1 - 10m < -1$ or $10 + 3m \le -5 \rightarrow m > 0$ or $m \le -5$

Job earnings comparison for Trinity between Blue Lakes and Silly Goats Coffee Shop:
- Lifeguard earnings expression at Blue Lakes ( $12$ per hour plus $24$ parking allowance): $12h + 24$
- Barista earnings expression at Silly Goats Coffee Shop ( $9$ per hour plus $45$ tips): $9h + 45$
- Equal earnings equation: $12h + 24 = 9h + 45$
- Calculated break-even hours: $h = 7\,\text{hours}$
- Total earnings at equal hours: $108$
School cafeteria lunch sales modeling:
- Cost per student lunch: $1.50$
- Revenue range: $1275$ to $1695$
- Compound inequality model: $1275 \le 1.50x \le 1695$
- Solved student range: $850 \le x \le 1130$
- Minimum student count for $1275$ revenue: At least $850$
- Maximum student count for $1695$ revenue: At most $1130$
Car purchase budget modeling for Jazzy:
- Budget limits: At least $14000$ and no more than $21000$
- Additional costs: $8\%$ sales tax, $20.5\%$ registration and inspection fees, minus a $150$ rebate
- Compound inequality model: $14000 \le 1.285x - 150 \le 21000$
- Solved sticker price range: $11011.67 \le x \le 16459.14$