1. **Problem 24:** Solve the inequality $3[1 + (-2)] + e \leq \frac{2e}{3}$. 2. First, simplify inside the brackets: $$3[1 + (-2)] = 3[-1] = -3$$ 3. Substitute back: $$-3 + e \leq \frac{2e}{3}$$ 4. Add 3 to both sides: $$\cancel{-3} + e + 3 \leq \frac{2e}{3} + 3$$ $$e \leq \frac{2e}{3} + 3$$ 5. Subtract $\frac{2e}{3}$ from both sides: $$e - \frac{2e}{3} \leq 3$$ $$\frac{3e}{3} - \frac{2e}{3} \leq 3$$ $$\frac{e}{3} \leq 3$$ 6. Multiply both sides by 3: $$e \leq 9$$ --- **Problem 25:** Solve $6s - 3 - 2s \geq 2s - 1.4$. 1. Simplify left side: $$6s - 2s - 3 \geq 2s - 1.4$$ $$4s - 3 \geq 2s - 1.4$$ 2. Add 3 to both sides: $$4s - 3 + 3 \geq 2s - 1.4 + 3$$ $$4s \geq 2s + 1.6$$ 3. Subtract $2s$ from both sides: $$4s - 2s \geq 1.6$$ $$2s \geq 1.6$$ 4. Divide both sides by 2: $$\cancel{2}s / \cancel{2} \geq \frac{1.6}{2}$$ $$s \geq 0.8$$ --- **Problem 26:** Solve $9h - 3 \frac{1}{5} \geq 10h + \frac{12}{5}$. 1. Convert mixed number to improper fraction: $$3 \frac{1}{5} = \frac{16}{5}$$ 2. Rewrite inequality: $$9h - \frac{16}{5} \geq 10h + \frac{12}{5}$$ 3. Subtract $10h$ from both sides: $$9h - 10h - \frac{16}{5} \geq \frac{12}{5}$$ $$-h - \frac{16}{5} \geq \frac{12}{5}$$ 4. Add $\frac{16}{5}$ to both sides: $$-h \geq \frac{12}{5} + \frac{16}{5}$$ $$-h \geq \frac{28}{5}$$ 5. Multiply both sides by $-1$ and reverse inequality: $$h \leq -\frac{28}{5}$$ --- **Problem 27:** Graph compound inequality $x > -3$ and $x \leq 1$. - This means $x$ is greater than $-3$ (open circle) and less than or equal to $1$ (closed circle). --- **Problem 28:** Graph compound inequality $x > 4$ or $x < -2$. - This means $x$ is either greater than $4$ (open circle) or less than $-2$ (open circle). --- **Problem 29:** Graph compound inequality $0 \leq x \leq 5$. - This means $x$ is between $0$ and $5$ inclusive (closed circles at both ends). --- **Problem 30:** Write compound inequality for graph: $-3 \geq n$ and $n \leq 1$. - This is $n \leq -3$ and $n \leq 1$. --- **Problem 31:** Write compound inequality for graph: $-4 \geq n$ and $n \leq 4$. - This is $n \leq -4$ and $n \leq 4$. --- **Problem 32:** Write compound inequality for graph: $n \leq -4$ or $7 \geq n$. - This is $n \leq -4$ or $n \leq 7$. --- **Problem 33:** Sum of two consecutive even numbers is greater than 66. Find least possible values. 1. Let first even number be $x$, second is $x+2$. 2. Inequality: $$x + (x+2) > 66$$ $$2x + 2 > 66$$ 3. Subtract 2: $$2x > 64$$ 4. Divide by 2: $$x > 32$$ 5. Least even integer greater than 32 is 34. 6. So numbers are 34 and 36. --- **Problem 34:** Susan completed 3 times as many art projects as Molly. Together more than 12 projects. Find Molly's projects. 1. Let Molly's projects be $m$. 2. Susan's projects: $3m$. 3. Inequality: $$m + 3m > 12$$ $$4m > 12$$ 4. Divide by 4: $$m > 3$$ 5. Molly completed more than 3 projects. --- **Problem 35:** Tony has 3 more than twice Peter's coins. Together fewer than 87 coins. Find Peter's coins. 1. Let Peter's coins be $p$. 2. Tony's coins: $2p + 3$. 3. Inequality: $$p + (2p + 3) < 87$$ $$3p + 3 < 87$$ 4. Subtract 3: $$3p < 84$$ 5. Divide by 3: $$p < 28$$ 6. Peter has fewer than 28 coins. --- **Problem 36:** Sum of two consecutive odd numbers at most 32. Find greatest possible values. 1. Let first odd number be $x$, second $x+2$. 2. Inequality: $$x + (x+2) \leq 32$$ $$2x + 2 \leq 32$$ 3. Subtract 2: $$2x \leq 30$$ 4. Divide by 2: $$x \leq 15$$ 5. Greatest odd number less than or equal to 15 is 15. 6. Numbers are 15 and 17. --- **Problem 37:** Of 184 parking places, fewer than 70 filled. How many not filled? 1. Filled places $< 70$. 2. Not filled $> 184 - 70 = 114$. 3. So more than 114 places not filled. --- **Problem 38:** 60 more boys than girls attended picnic. At most 230 boys. Find girls. 1. Let girls be $g$. 2. Boys: $g + 60$. 3. Inequality: $$g + 60 \leq 230$$ 4. Subtract 60: $$g \leq 170$$ 5. At most 170 girls attended.