1. **State the problem:** Solve the inequality $3b \leq 9$ and graph it on the number line. 2. **Formula and rules:** To solve inequalities, isolate the variable by performing inverse operations. Remember, when multiplying or dividing by a negative number, reverse the inequality sign. 3. **Solve $3b \leq 9$:** $$3b \leq 9$$ Divide both sides by 3: $$\frac{\cancel{3}b}{\cancel{3}} \leq \frac{9}{3}$$ $$b \leq 3$$ 4. **Interpretation:** The solution is all values of $b$ less than or equal to 3. 5. **Graph:** On the number line, shade all values to the left of 3 including 3. 1. **State the problem:** Solve the inequality $8 < \frac{x}{2}$ and graph it. 2. **Solve $8 < \frac{x}{2}$:** Multiply both sides by 2: $$8 \times 2 < \frac{x}{2} \times 2$$ $$16 < x$$ 3. **Interpretation:** $x$ is greater than 16. 4. **Graph:** On the number line, shade all values to the right of 16, not including 16. 1. **State the problem:** For $5k > 100$, check if 20 and 100 are solutions. 2. **Check $k=20$:** $$5 \times 20 = 100$$ Since $100 \not> 100$, 20 is NOT a solution. 3. **Check $k=100$:** $$5 \times 100 = 500$$ Since $500 > 100$, 100 is a solution. 1. **State the problem:** For $u + 5 \leq 6$, check if 0 and 1 are solutions. 2. **Check $u=0$:** $$0 + 5 = 5 \leq 6$$ True, so 0 is a solution. 3. **Check $u=1$:** $$1 + 5 = 6 \leq 6$$ True, so 1 is a solution. **Final answers:** - $3b \leq 9$ solution: $b \leq 3$ - $8 < \frac{x}{2}$ solution: $x > 16$ - For $5k > 100$, 20 is NOT a solution, 100 is a solution. - For $u + 5 \leq 6$, both 0 and 1 are solutions.